Differential equation solutions with MATLAB
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| 245 | 1 | 0 | |a Differential equation solutions with MATLAB |c Dingyü Xue |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2020] | |
| 264 | 4 | |a [Beijing] |b Tsinghua University Press |c [2020] | |
| 264 | 4 | |c © 2020 | |
| 300 | |a XIII, 438 Seiten |b Illustrationen, Diagramme | ||
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| 490 | 0 | |a De Gruyter STEM | |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a MATLAB |0 (DE-588)4329066-8 |D s |
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| adam_text | CONTENTS
PREFACE
*
V
1
1.1
1.1.1
1.1.2
1.1.3
1.2
1.3
1.4
AN
INTRODUCTION
TO
DIFFERENTIAL
EQUATIONS
*
1
INTRODUCTION
TO
DIFFERENTIAL
EQUATION
MODELING
*
1
MODELING
OF
AN
ELECTRIC
CIRCUIT
*
1
MODELING
IN
MECHANICAL
SYSTEMS
*
3
MODELS
IN
SOCIAL
SYSTEMS
*
4
A
BRIEF
HISTORY
OF
DIFFERENTIAL
EQUATIONS
*
6
OUTLINE
AND
MAIN
TOPICS
IN
THE
BOOK
*
8
EXERCISES
*
10
2
2.1
2.1.1
2.1.2
2.1.3
2.1.4
2.2
2.2.1
2.2.2
2.2.3
2.2.4
2.2.5
2.3
ANALYTICAL
SOLUTIONS
OF
ORDINARY
DIFFERENTIAL
EQUATIONS
*
11
ANALYTICAL
SOLUTIONS
OF
FIRST-ORDER
DIFFERENTIAL
EQUATIONS
*
11
DIFFERENTIAL
EQUATION
SOLVABLE
BY
SIMPLE
INTEGRALS
*
12
HOMOGENEOUS
DIFFERENTIAL
EQUATIONS
*
13
INHOMOGENEOUS
LINEAR
DIFFERENTIAL
EQUATIONS
*
14
NONLINEAR
DIFFERENTIAL
EQUATIONS
WITH
SEPARABLE
VARIABLES
*
15
SPECIAL
FUNCTIONS
AND
SECOND-ORDER
DIFFERENTIAL
EQUATIONS
*
17
GAMMA
FUNCTION
*
17
HYPERGEOMETRIC
FUNCTIONS
*
19
BESSEL
DIFFERENTIAL
EQUATIONS
*
20
LEGENDRE
DIFFERENTIAL
EQUATIONS
AND
FUNCTIONS
*
22
AIRY
FUNCTIONS
-----
23
SOLUTIONS
OF
LINEAR
DIFFERENTIAL
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
*
25
2.3.1
MATHEMATICAL
MODELING
OF
LINEAR
CONSTANT-COEFFICIENT
DIFFERENTIAL
EQUATIONS
*
25
2.3.2
2.3.3
2.3.4
2.4
2.4.1
2.4.2
LAPLACE
TRANSFORM-BASED
SOLUTIONS
*
26
SOLUTIONS
OF
INHOMOGENEOUS
DIFFERENTIAL
EQUATIONS
*
28
SOLUTIONS
OF
DIFFERENTIAL
EQUATIONS
WITH
NONZERO
INITIAL
VALUES
*
29
ANALYTICAL
SOLUTIONS
OF
ORDINARY
DIFFERENTIAL
EQUATIONS
*
32
ANALYTICAL
SOLUTIONS
OF
SIMPLE
DIFFERENTIAL
EQUATIONS
*
32
ANALYTICAL
SOLUTIONS
OF
HIGH-ORDER
LINEAR
DIFFERENTIAL
EQUATIONS
WITH
CONSTANT COEFFICIENTS
*
35
2.4.3
2.4.4
2.4.5
2.5
2.5.1
2.5.2
ANALYTICAL SOLUTIONS
OF
LINEAR
TIME-VARYING
DIFFERENTIAL
EQUATIONS
*
38
SOLUTIONS
OF
TIME-VARYING
DIFFERENTIAL
EQUATION
SETS
*
40
SOLUTIONS
OF
BOUNDARY
VALUE
PROBLEMS
*
41
SOLUTIONS
OF
LINEAR
MATRIX
DIFFERENTIAL
EQUATIONS
*
42
ANALYTICAL
SOLUTIONS
OF
LINEAR
STATE
SPACE
EQUATIONS
*
43
DIRECT
SOLUTIONS
OF
STATE
SPACE
MODELS
*
45
VIII
*
CONTENTS
2.5.3
2.5.4
SOLUTION
OF
SYLVESTER
DIFFERENTIAL
EQUATION
*
46
KRONECKER
PRODUCT-BASED
SOLUTIONS
OF
SYLVESTER
DIFFERENTIAL
EQUATIONS
*
47
2.6
2.6.1
2.6.2
ANALYTICAL
SOLUTIONS
TO
SPECIAL
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
48
SOLVABLE
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
48
NONLINEAR
DIFFERENTIAL
EQUATIONS
WHERE
ANALYTICAL
SOLUTIONS
ARE
NOT
AVAILABLE
*
50
2.7
EXERCISES
*
51
3
3.1
INITIAL
VALUE
PROBLEMS
*
55
INITIAL
VALUE
DESCRIPTIONS
FOR
FIRST-ORDER
EXPLICIT
DIFFERENTIAL
EQUATIONS
*
55
3.1.1
3.1.2
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.2.5
3.2.6
3.3
3.3.1
3.3.2
3.3.3
3.3.4
3.3.5
3.3.6
3.4
3.4.1
3.4.2
3.4.3
3.4.4
3.4.5
3.5
MATHEMATICAL
FORMS
OF
INITIAL
VALUE
PROBLEMS
*
55
EXISTENCE
AND
UNIQUENESS
OF
SOLUTIONS
*
56
IMPLEMENTATION
OF
FIXED-STEP
NUMERICAL
ALGORITHMS
*
57
EULER
*
S
METHOD
*
57
SECOND-ORDER
RUNGE-KUTTA
ALGORITHM
*
60
FOURTH-ORDER
RUNGE-KUTTA
ALGORITHM
*
62
GILL
*
S
ALGORITHM
*
64
THE
MTH
ORDER
RUNGE-KUTTA
ALGORITHM
*
65
MULTISTEP
ALGORITHMS
AND
IMPLEMENTATION
*
68
VARIABLE-STEP
NUMERICAL
ALGORITHMS
AND
IMPLEMENTATIONS
*
70
MEASURES
TO
INCREASE
EFFICIENCY
*
71
AN
INTRODUCTION
TO
VARIABLE-STEP
ALGORITHMS
*
72
THE
4/5TH
ORDER
RUNGE-KUTTA
VARIABLE-STEP
ALGORITHM
*
73
THE
DIFFERENTIAL
EQUATION
SOLVER
PROVIDED
IN
MATLAB
*
74
SOLUTIONS
OF
DIFFERENTIAL
EQUATIONS
WITH
ADDITIONAL
PARAMETERS
*
80
AVOIDING
THE
USE
OF
ADDITIONAL
PARAMETERS
*
82
VALIDATIONS
OF
NUMERICAL
SOLUTIONS
*
83
VALIDATION
OF
THE
COMPUTATION
RESULTS
*
83
DYNAMIC
MANIPULATION
OF
INTERMEDIATE
RESULTS
*
86
MORE
ACCURATE
SOLVERS
*
87
STEP-SIZES
AND
FIXED-STEP
DISPLAY
*
88
DEMONSTRATIONS
OF
HIGH-ORDER
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
91
EXERCISES
*
93
4
4.1
4.1.1
4.1.2
4.1.3
4.1.4
STANDARD
FORM
CONVERSIONS
OF
ORDINARY
DIFFERENTIAL
EQUATIONS
*
99
CONVERSION
METHOD
FOR
A
SINGLE
HIGH-ORDER
DIFFERENTIAL
EQUATION
*
99
CONVERSION
OF
EXPLICIT
EQUATIONS
*
100
SOLUTIONS
OF
TIME-VARYING
DIFFERENTIAL
EQUATIONS
*
104
SINGULARITIES
IN
DIFFERENTIAL
EQUATIONS
*
106
STATE
AUGMENTATION
FOR
CONSTANT
PARAMETERS
*
108
CONTENTS
*
IX
4.2
CONVERSIONS
OF
COMPLICATED
HIGH-ORDER
DIFFERENTIAL
EQUATIONS
*
109
4.2.1
EQUATIONS
CONTAINING
THE
SQUARE
OF
THE
HIGHEST-ORDER
DERIVATIVE
*
110
4.2.2
EQUATIONS
CONTAINING
ODD
POWERS
*
112
4.2.3
EQUATIONS
CONTAINING
NONLINEAR
OPERATIONS
*
113
4.3
CONVERSIONS
OF
DIFFERENTIAL
EQUATION
SETS
*
114
4.3.1
SIMPLE
EXPLICIT
DIFFERENTIAL
EQUATION
SETS
*
115
4.3.2
LIMITATIONS
WITH
FIXED-STEP
METHODS
*
122
4.3.3
SIMPLE
IMPLICIT
DIFFERENTIAL
EQUATIONS
*
124
4.3.4
EVEN
MORE
COMPLICATED
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
127
4.4
CONVERSIONS
FOR
MATRIX
DIFFERENTIAL
EQUATIONS
*
129
4.4.1
CONVERSION
AND
SOLUTIONS
OF
DIFFERENTIAL
EQUATIONS
IN
MATRIX
FORM
-----
129
4.4.2
SYLVESTER
DIFFERENTIAL
EQUATIONS
*
132
4.4.3
RICCATI
DIFFERENTIAL
EQUATIONS
*
133
4.5
CONVERSIONS
OF
A
CLASS
OF
VOLTERRA
INTEGRO-DIFFERENTIAL
EQUATIONS
*
135
4.6
EXERCISES
*
139
5
SPECIAL
DIFFERENTIAL
EQUATIONS
*
145
5.1
STIFF
DIFFERENTIAL
EQUATIONS
*
145
5.1.1
TIME
CONSTANTS
IN
LINEAR
DIFFERENTIAL
EQUATIONS
*
146
5.1.2
DEMONSTRATIONS
OF
STIFF
PHENOMENA
*
146
5.1.3
DIRECT
SOLUTION
OF
STIFF
DIFFERENTIAL
EQUATIONS
*
149
5.1.4
STIFFNESS
DETECTION
*
152
5.1.5
FIXED-STEP
SOLUTION
OF
STIFF
DIFFERENTIAL
EQUATIONS
*
157
5.2
IMPLICIT
DIFFERENTIAL
EQUATIONS
*
158
5.2.1
MATHEMATICAL
DESCRIPTION
OF
IMPLICIT
DIFFERENTIAL
EQUATIONS
*
159
5.2.2
CONSISTENT
INITIAL
VALUE
TRANSFORMATION
*
160
5.2.3
DIRECT
SOLUTION
OF
IMPLICIT
DIFFERENTIAL
EQUATIONS
*
163
5.2.4
IMPLICIT
DIFFERENTIAL
EQUATIONS
WITH
MULTIPLE
SOLUTIONS
*
166
5.3
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
168
5.3.1
GENERAL
FORM
OF
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
168
5.3.2
INDICES
OF
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
169
5.3.3
SEMI-EXPLICIT DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
169
5.3.4
LIMITATIONS
OF
THE
DIRECT
SOLVER
*
173
5.3.5
IMPLICIT
SOLVERS
FOR
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
175
5.3.6
INDEX
REDUCTION
FOR
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
180
5.4
SWITCHED
DIFFERENTIAL
EQUATIONS
*
183
5.4.1 LINEAR
SWITCHED
DIFFERENTIAL
EQUATIONS
*
183
5.4.2 ZERO-CROSSING
DETECTION
AND
EVENT
HANDLING
*
185
5.4.3
NONLINEAR
SWITCHED
DIFFERENTIAL
EQUATIONS
*
188
5.4.4
DISCONTINUOUS
DIFFERENTIAL
EQUATIONS
*
190
5.5
LINEAR
STOCHASTIC
DIFFERENTIAL
EQUATIONS
*
191
X
*
CONTENTS
5.5.1
TRANSFER
FUNCTION
MODEL
FOR
LINEAR
STOCHASTIC
DIFFERENTIAL
EQUATIONS
*
192
5.5.2
5.5.3
5.6
ERRONEOUS
METHODS
IN
CONTINUOUS
STOCHASTIC
SYSTEM
SIMULATION
*
193
DISCRETIZING
STOCHASTIC
LINEAR
SYSTEMS
*
195
EXERCISES
*
199
6
6.1
DELAY
DIFFERENTIAL
EQUATIONS
*
205
NUMERICAL
SOLUTIONS
OF
DELAY
DIFFERENTIAL
EQUATIONS
WITH
CONSTANT
DELAYS
-----
205
6.1.1
6.1.2
6.1.3
6.2
6.2.1
6.2.2
6.2.3
6.2.4
6.3
6.3.1
6.3.2
6.4
6.5
ORDINARY
AND
DELAY
DIFFERENTIAL
EQUATIONS
*
205
DELAY
DIFFERENTIAL
EQUATION
WITH
ZERO
HISTORY
FUNCTIONS
*
207
NONZERO
HISTORY
FUNCTIONS
*
212
DIFFERENTIAL
EQUATIONS
WITH
VARIABLE
DELAYS
*
214
VARIABLE
DELAY MODELS
*
215
TIME-DEPENDENT
DELAYS
*
215
STATE-DEPENDENT
DELAYS
*
219
DELAY
DIFFERENTIAL
EQUATIONS
WITH
GENERALIZED
DELAYS
*
221
NEUTRAL-TYPE
DELAY
DIFFERENTIAL
EQUATIONS
*
222
NEUTRAL-TYPE
EQUATIONS
*
223
NEUTRAL-TYPE
DIFFERENTIAL
EQUATIONS
WITH
VARIABLE
DELAYS
*
226
VOLTERRA
DIFFERENTIAL
EQUATIONS
WITH
DELAYS
*
228
EXERCISES
*
229
7
7.1
7.1.1
PROPERTIES
AND
BEHAVIORS
OF
ORDINARY
DIFFERENTIAL
EQUATIONS
*
233
STABILITY
OF
DIFFERENTIAL
EQUATIONS
*
233
STABILITY
OF
LINEAR
DIFFERENTIAL
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
*
233
7.1.2
7.1.3
7.1.4
7.1.5
7.1.6
ROUTH-HURWITZ
STABILITY
CRITERION
*
236
LYAPUNOV
FUNCTION
AND
LYAPUNOV
STABILITY
*
239
AUTONOMOUS
CONVERSION
OF
TIME-VARYING
DIFFERENTIAL
EQUATIONS
*
240
STABILITY
ASSESSMENT
OF
NONLINEAR
SYSTEMS
BY
EXAMPLES
*
241
STABILITY
ASSESSMENT
OF
COMPLICATED
SYSTEMS
WITH
SIMULATION
METHODS
-----
243
7.2
7.2.1
7.2.2
7.2.3
7.2.4
7.3
7.3.1
7.3.2
7.3.3
SPECIAL
BEHAVIORS
OF
DIFFERENTIAL
EQUATIONS
*
246
LIMIT
CYCLES
*
246
PERIODIC
SOLUTIONS
*
251
CHAOS
AND
ATTRACTORS
*
254
POINCARE
MAPPING
*
259
LINEARIZATION
APPROXIMATION
OF
DIFFERENTIAL
EQUATIONS
*
261
EQUILIBRIUM
POINTS
-----
261
LINEARIZATION
OF
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
265
PROPERTIES
OF
EQUILIBRIA
*
269
CONTENTS
*
XI
7.4
7.5
BIFURCATION
OF
DIFFERENTIAL
EQUATIONS
*
269
EXERCISES
*
270
8
8.1
8.1.1
8.1.2
FRACTIONAL-ORDER
DIFFERENTIAL
EQUATIONS
*
273
DEFINITIONS
AND
NUMERICAL COMPUTATION
IN
FRACTIONAL
CALCULUS
*
273
DEFINITIONS
OF
FRACTIONAL
CALCULUS
*
274
RELATIONSHIPS
AND
PROPERTIES
OF
DIFFERENT
FRACTIONAL
CALCULUS
DEFINITIONS
*
275
8.1.3
8.1.4
8.2
NUMERICAL
COMPUTATION
FOR
GRUNWALD-LETNIKOV
DERIVATIVES
*
277
NUMERICAL
COMPUTATION
FOR
CAPUTO
DERIVATIVES
*
277
ANALYTICAL
SOLUTION
OF
LINEAR
COMMENSURATE-ORDER
DIFFERENTIAL
EQUATIONS
*
279
8.2.1
8.2.2
8.2.3
8.2.4
8.3
MITTAG-LEFFLER
FUNCTIONS
*
279
COMMENSURATE-ORDER
LINEAR
DIFFERENTIAL
EQUATIONS
*
280
AN
IMPORTANT
LAPLACE
TRANSFORM
FORMULA
*
281
PARTIAL
FRACTION
EXPANSION-BASED
ANALYTICAL
APPROACH
*
282
NUMERICAL
SOLUTIONS
OF
LINEAR
FRACTIONAL-ORDER
DIFFERENTIAL
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
*
287
8.3.1
8.3.2
8.3.3
8.3.4
8.3.5
8.4
8.4.1
8.4.2
8.4.3
8.5
A
CLOSED-FORM
SOLUTION
*
287
RIEMANN-LIOUVILLE
DIFFERENTIAL
EQUATIONS
*
289
CAPUTO
DIFFERENTIAL
EQUATIONS
*
291
COMPUTING
EQUIVALENT
INITIAL
VALUES
*
294
HIGH
PRECISION
ALGORITHMS
*
297
SOLUTION
OF
NONLINEAR
FRACTIONAL-ORDER
DIFFERENTIAL
EQUATIONS
*
300
PREDICTOR
METHOD
*
300
CORRECTOR
METHOD
*
304
MATRIX
METHOD
FOR
IMPLICIT
CAPUTO
DIFFERENTIAL
EQUATIONS
*
305
EXERCISES
*
308
9
9.1
9.1.1
9.1.2
9.2
BLOCK
DIAGRAM
SOLUTIONS
OF
ORDINARY
DIFFERENTIAL
EQUATIONS
*
311
SIMULINK
ESSENTIALS
*
312
AN
INTRODUCTION
TO
SIMULINK
*
312
RELEVANT
BLOCKS
IN
SIMULINK
*
312
BLOCK
DIAGRAM
MODELING
METHODOLOGIES
IN
DIFFERENTIAL
EQUATIONS
-----
314
9.2.1
9.2.2
9.2.3
9.2.4
9.3
9.3.1
9.3.2
INTEGRATOR
CHAINS
AND
KEY
SIGNAL
GENERATION
*
314
DIFFERENTIAL
EQUATION
DESCRIPTION
METHODS
*
315
SOLUTIONS
OF
DIFFERENTIAL
EQUATIONS
*
318
ALGORITHMS
AND
PARAMETER
SETTINGS
*
319
MODELING
EXAMPLES
OF
DIFFERENTIAL
EQUATIONS
*
321
SIMPLE
DIFFERENTIAL
EQUATIONS
*
321
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
325
XII
*
CONTENTS
9.3.3
SWITCHED
DIFFERENTIAL
EQUATIONS
*
327
9.3.4
DISCONTINUOUS
DIFFERENTIAL
EQUATIONS
*
330
9.3.5
DELAY
DIFFERENTIAL
EQUATIONS
*
330
9.3.6
DELAY
DIFFERENTIAL
EQUATIONS
WITH
NONZERO
HISTORY
FUNCTIONS
*
333
9.3.7
STOCHASTIC
DIFFERENTIAL
EQUATIONS
*
334
9.4
SIMULINK
MODELING
OF
FRACTIONAL-ORDER
DIFFERENTIAL
EQUATIONS
*
336
9.4.1
FRACTIONAL-ORDER
OPERATOR
BLOCK
*
337
9.4.2
MODELING
AND
SOLUTION
OF
RIEMANN-LIOUVILLE
DIFFERENTIAL
EQUATIONS
*
339
9.4.3
BLOCK
FOR
CAPUTO
DERIVATIVES
*
341
9.4.4
MODELING
AND
SOLVING
OF
CAPUTO
DIFFERENTIAL
EQUATIONS
*
341
9.4.5
FRACTIONAL-ORDER
DELAY
DIFFERENTIAL
EQUATIONS
*
344
9.5
EXERCISES
*
346
10
BOUNDARY
VALUE
PROBLEMS
FOR
ORDINARY
DIFFERENTIAL
EQUATIONS
*
349
10.1
STANDARD
BOUNDARY
VALUE
PROBLEMS
*
349
10.2
SHOOTING
METHODS
IN
TWO-POINT
BOUNDARY
VALUE
PROBLEMS
FOR
SECOND-ORDER
DIFFERENTIAL
EQUATIONS
*
350
10.2.1
SHOOTING
ALGORITHMS
FOR
LINEAR
TIME-VARYING
DIFFERENTIAL
EQUATIONS
*
351
10.2.2
FINITE
DIFFERENCE
ALGORITHM
FOR
LINEAR
DIFFERENTIAL
EQUATIONS
*
354
10.2.3
SHOOTING
ALGORITHMS
FOR
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
357
10.3
TWO-POINT
BOUNDARY
VALUE
PROBLEMS
FOR
HIGH-ORDER
DIFFERENTIAL
EQUATIONS
*
360
10.3.1
DIRECT
SOLVER
IN
MATLAB
*
361
10.3.2
SOLUTION
OF
SIMPLE
BOUNDARY
VALUE
PROBLEMS
*
362
10.3.3
DESCRIPTIONS
OF
COMPLICATED
BOUNDARY
CONDITIONS
*
366
10.3.4
BOUNDARY
VALUE
PROBLEMS
WITH
UNDETERMINED
COEFFICIENTS
*
368
10.3.5
BOUNDARY
VALUE
PROBLEMS
WITH
SEMI-INFINITE
INTERVALS
*
370
10.3.6
DIFFERENTIAL
EQUATIONS
WITH
FLOATING
BOUNDARY
VALUES
*
372
10.3.7
BOUNDARY
VALUE
PROBLEMS
OF
INTEGRO-DIFFERENTIAL
EQUATIONS
*
373
10.4
OPTIMIZATION-BASED
BOUNDARY
VALUE
PROBLEM
SOLUTIONS
*
374
10.4.1
ILLUSTRATIVE
EXAMPLE
TO
SIMPLE
BOUNDARY
VALUE
PROBLEMS
*
375
10.4.2
BOUNDARY
VALUE
PROBLEMS
FOR
IMPLICIT
DIFFERENTIAL
EQUATIONS
*
376
10.4.3
BOUNDARY
VALUE
PROBLEMS
FOR
DELAY
DIFFERENTIAL
EQUATIONS
*
379
10.4.4
MULTIPOINT
BOUNDARY
VALUE
PROBLEMS
*
381
10.4.5
FLOATING
BOUNDARY
VALUE
PROBLEMS
REVISITED
*
383
10.4.6
BOUNDARY
VALUE
PROBLEMS
FOR
BLOCK
DIAGRAMS
*
384
10.4.7
BOUNDARY
VALUE
PROBLEMS
FOR
FRACTIONAL-ORDER
DIFFERENTIAL
EQUATIONS
*
386
10.5
EXERCISES
------
387
CONTENTS
*
XIII
11
PARTIAL
DIFFERENTIAL
EQUATIONS
*
391
11.1
NUMERICAL
SOLUTIONS
OF
DIFFUSION
EQUATIONS
*
392
11.1.1
MATHEMATICAL
FORM
AND
ANALYTICAL
SOLUTIONS
OF
ONE-DIMENSIONAL
DIFFUSION
EQUATIONS
*
392
11.1.2
DISCRETIZING
DIFFUSION
EQUATIONS
-----
393
11.1.3
INHOMOGENEOUS
DIFFUSION
EQUATIONS
*
397
11.1.4
MULTIDIMENSIONAL
DIFFUSION
EQUATIONS
*
399
11.2
SEVERAL
SPECIAL
FORMS
OF
PARTIAL
DIFFERENTIAL
EQUATIONS
*
399
11.2.1
CLASSIFICATION
OF
PARTIAL
DIFFERENTIAL
EQUATIONS
*
400
11.2.2
EIGENVALUE-TYPE
PARTIAL
DIFFERENTIAL
EQUATIONS
*
401
11.2.3
CLASSIFICATION
OF
BOUNDARY
CONDITIONS
*
402
11.3
USER
INTERFACE
OF
TYPICAL
TWO-DIMENSIONAL
PARTIAL
DIFFERENTIAL
EQUATIONS
*
402
11.3.1
AN
INTRODUCTION
OF
THE
USER
INTERFACE
*
402
11.3.2
GEOMETRIC
REGION
DESIGN
*
404
11.3.3
BOUNDARY
CONDITION
DESCRIPTION
*
405
11.3.4
EXAMPLES
OF
PARTIAL
DIFFERENTIAL
EQUATION
SOLUTIONS
*
406
11.3.5
OTHER
SOLUTION
DISPLAY
METHODS
*
407
11.3.6
PARTIAL
DIFFERENTIAL
EQUATIONS
WITH
FUNCTIONAL
COEFFICIENTS
*
409
11.4
SOLUTIONS
OF
PARTIAL
DIFFERENTIAL
EQUATIONS
*
410
11.4.1
CREATING
A
BLANK
PARTIAL
DIFFERENTIAL
EQUATION
OBJECT
*
411
11.4.2
STATEMENT
DESCRIPTION
OF
GEOMETRIC
REGIONS
*
411
11.4.3
BOUNDARY
AND
INITIAL
CONDITION
DESCRIPTIONS
*
415
11.4.4
PARTIAL
DIFFERENTIAL
EQUATIONS
DESCRIPTIONS
*
415
11.4.5
NUMERICAL
SOLUTIONS
OF
PARTIAL
DIFFERENTIAL
EQUATIONS
*
417
11.5
EXERCISES
*
423
BIBLIOGRAPHY
*
425
MATLAB
FUNCTION
INDEX
*
429
INDEX
-----
433
|
| adam_txt |
CONTENTS
PREFACE
*
V
1
1.1
1.1.1
1.1.2
1.1.3
1.2
1.3
1.4
AN
INTRODUCTION
TO
DIFFERENTIAL
EQUATIONS
*
1
INTRODUCTION
TO
DIFFERENTIAL
EQUATION
MODELING
*
1
MODELING
OF
AN
ELECTRIC
CIRCUIT
*
1
MODELING
IN
MECHANICAL
SYSTEMS
*
3
MODELS
IN
SOCIAL
SYSTEMS
*
4
A
BRIEF
HISTORY
OF
DIFFERENTIAL
EQUATIONS
*
6
OUTLINE
AND
MAIN
TOPICS
IN
THE
BOOK
*
8
EXERCISES
*
10
2
2.1
2.1.1
2.1.2
2.1.3
2.1.4
2.2
2.2.1
2.2.2
2.2.3
2.2.4
2.2.5
2.3
ANALYTICAL
SOLUTIONS
OF
ORDINARY
DIFFERENTIAL
EQUATIONS
*
11
ANALYTICAL
SOLUTIONS
OF
FIRST-ORDER
DIFFERENTIAL
EQUATIONS
*
11
DIFFERENTIAL
EQUATION
SOLVABLE
BY
SIMPLE
INTEGRALS
*
12
HOMOGENEOUS
DIFFERENTIAL
EQUATIONS
*
13
INHOMOGENEOUS
LINEAR
DIFFERENTIAL
EQUATIONS
*
14
NONLINEAR
DIFFERENTIAL
EQUATIONS
WITH
SEPARABLE
VARIABLES
*
15
SPECIAL
FUNCTIONS
AND
SECOND-ORDER
DIFFERENTIAL
EQUATIONS
*
17
GAMMA
FUNCTION
*
17
HYPERGEOMETRIC
FUNCTIONS
*
19
BESSEL
DIFFERENTIAL
EQUATIONS
*
20
LEGENDRE
DIFFERENTIAL
EQUATIONS
AND
FUNCTIONS
*
22
AIRY
FUNCTIONS
-----
23
SOLUTIONS
OF
LINEAR
DIFFERENTIAL
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
*
25
2.3.1
MATHEMATICAL
MODELING
OF
LINEAR
CONSTANT-COEFFICIENT
DIFFERENTIAL
EQUATIONS
*
25
2.3.2
2.3.3
2.3.4
2.4
2.4.1
2.4.2
LAPLACE
TRANSFORM-BASED
SOLUTIONS
*
26
SOLUTIONS
OF
INHOMOGENEOUS
DIFFERENTIAL
EQUATIONS
*
28
SOLUTIONS
OF
DIFFERENTIAL
EQUATIONS
WITH
NONZERO
INITIAL
VALUES
*
29
ANALYTICAL
SOLUTIONS
OF
ORDINARY
DIFFERENTIAL
EQUATIONS
*
32
ANALYTICAL
SOLUTIONS
OF
SIMPLE
DIFFERENTIAL
EQUATIONS
*
32
ANALYTICAL
SOLUTIONS
OF
HIGH-ORDER
LINEAR
DIFFERENTIAL
EQUATIONS
WITH
CONSTANT COEFFICIENTS
*
35
2.4.3
2.4.4
2.4.5
2.5
2.5.1
2.5.2
ANALYTICAL SOLUTIONS
OF
LINEAR
TIME-VARYING
DIFFERENTIAL
EQUATIONS
*
38
SOLUTIONS
OF
TIME-VARYING
DIFFERENTIAL
EQUATION
SETS
*
40
SOLUTIONS
OF
BOUNDARY
VALUE
PROBLEMS
*
41
SOLUTIONS
OF
LINEAR
MATRIX
DIFFERENTIAL
EQUATIONS
*
42
ANALYTICAL
SOLUTIONS
OF
LINEAR
STATE
SPACE
EQUATIONS
*
43
DIRECT
SOLUTIONS
OF
STATE
SPACE
MODELS
*
45
VIII
*
CONTENTS
2.5.3
2.5.4
SOLUTION
OF
SYLVESTER
DIFFERENTIAL
EQUATION
*
46
KRONECKER
PRODUCT-BASED
SOLUTIONS
OF
SYLVESTER
DIFFERENTIAL
EQUATIONS
*
47
2.6
2.6.1
2.6.2
ANALYTICAL
SOLUTIONS
TO
SPECIAL
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
48
SOLVABLE
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
48
NONLINEAR
DIFFERENTIAL
EQUATIONS
WHERE
ANALYTICAL
SOLUTIONS
ARE
NOT
AVAILABLE
*
50
2.7
EXERCISES
*
51
3
3.1
INITIAL
VALUE
PROBLEMS
*
55
INITIAL
VALUE
DESCRIPTIONS
FOR
FIRST-ORDER
EXPLICIT
DIFFERENTIAL
EQUATIONS
*
55
3.1.1
3.1.2
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.2.5
3.2.6
3.3
3.3.1
3.3.2
3.3.3
3.3.4
3.3.5
3.3.6
3.4
3.4.1
3.4.2
3.4.3
3.4.4
3.4.5
3.5
MATHEMATICAL
FORMS
OF
INITIAL
VALUE
PROBLEMS
*
55
EXISTENCE
AND
UNIQUENESS
OF
SOLUTIONS
*
56
IMPLEMENTATION
OF
FIXED-STEP
NUMERICAL
ALGORITHMS
*
57
EULER
*
S
METHOD
*
57
SECOND-ORDER
RUNGE-KUTTA
ALGORITHM
*
60
FOURTH-ORDER
RUNGE-KUTTA
ALGORITHM
*
62
GILL
*
S
ALGORITHM
*
64
THE
MTH
ORDER
RUNGE-KUTTA
ALGORITHM
*
65
MULTISTEP
ALGORITHMS
AND
IMPLEMENTATION
*
68
VARIABLE-STEP
NUMERICAL
ALGORITHMS
AND
IMPLEMENTATIONS
*
70
MEASURES
TO
INCREASE
EFFICIENCY
*
71
AN
INTRODUCTION
TO
VARIABLE-STEP
ALGORITHMS
*
72
THE
4/5TH
ORDER
RUNGE-KUTTA
VARIABLE-STEP
ALGORITHM
*
73
THE
DIFFERENTIAL
EQUATION
SOLVER
PROVIDED
IN
MATLAB
*
74
SOLUTIONS
OF
DIFFERENTIAL
EQUATIONS
WITH
ADDITIONAL
PARAMETERS
*
80
AVOIDING
THE
USE
OF
ADDITIONAL
PARAMETERS
*
82
VALIDATIONS
OF
NUMERICAL
SOLUTIONS
*
83
VALIDATION
OF
THE
COMPUTATION
RESULTS
*
83
DYNAMIC
MANIPULATION
OF
INTERMEDIATE
RESULTS
*
86
MORE
ACCURATE
SOLVERS
*
87
STEP-SIZES
AND
FIXED-STEP
DISPLAY
*
88
DEMONSTRATIONS
OF
HIGH-ORDER
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
91
EXERCISES
*
93
4
4.1
4.1.1
4.1.2
4.1.3
4.1.4
STANDARD
FORM
CONVERSIONS
OF
ORDINARY
DIFFERENTIAL
EQUATIONS
*
99
CONVERSION
METHOD
FOR
A
SINGLE
HIGH-ORDER
DIFFERENTIAL
EQUATION
*
99
CONVERSION
OF
EXPLICIT
EQUATIONS
*
100
SOLUTIONS
OF
TIME-VARYING
DIFFERENTIAL
EQUATIONS
*
104
SINGULARITIES
IN
DIFFERENTIAL
EQUATIONS
*
106
STATE
AUGMENTATION
FOR
CONSTANT
PARAMETERS
*
108
CONTENTS
*
IX
4.2
CONVERSIONS
OF
COMPLICATED
HIGH-ORDER
DIFFERENTIAL
EQUATIONS
*
109
4.2.1
EQUATIONS
CONTAINING
THE
SQUARE
OF
THE
HIGHEST-ORDER
DERIVATIVE
*
110
4.2.2
EQUATIONS
CONTAINING
ODD
POWERS
*
112
4.2.3
EQUATIONS
CONTAINING
NONLINEAR
OPERATIONS
*
113
4.3
CONVERSIONS
OF
DIFFERENTIAL
EQUATION
SETS
*
114
4.3.1
SIMPLE
EXPLICIT
DIFFERENTIAL
EQUATION
SETS
*
115
4.3.2
LIMITATIONS
WITH
FIXED-STEP
METHODS
*
122
4.3.3
SIMPLE
IMPLICIT
DIFFERENTIAL
EQUATIONS
*
124
4.3.4
EVEN
MORE
COMPLICATED
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
127
4.4
CONVERSIONS
FOR
MATRIX
DIFFERENTIAL
EQUATIONS
*
129
4.4.1
CONVERSION
AND
SOLUTIONS
OF
DIFFERENTIAL
EQUATIONS
IN
MATRIX
FORM
-----
129
4.4.2
SYLVESTER
DIFFERENTIAL
EQUATIONS
*
132
4.4.3
RICCATI
DIFFERENTIAL
EQUATIONS
*
133
4.5
CONVERSIONS
OF
A
CLASS
OF
VOLTERRA
INTEGRO-DIFFERENTIAL
EQUATIONS
*
135
4.6
EXERCISES
*
139
5
SPECIAL
DIFFERENTIAL
EQUATIONS
*
145
5.1
STIFF
DIFFERENTIAL
EQUATIONS
*
145
5.1.1
TIME
CONSTANTS
IN
LINEAR
DIFFERENTIAL
EQUATIONS
*
146
5.1.2
DEMONSTRATIONS
OF
STIFF
PHENOMENA
*
146
5.1.3
DIRECT
SOLUTION
OF
STIFF
DIFFERENTIAL
EQUATIONS
*
149
5.1.4
STIFFNESS
DETECTION
*
152
5.1.5
FIXED-STEP
SOLUTION
OF
STIFF
DIFFERENTIAL
EQUATIONS
*
157
5.2
IMPLICIT
DIFFERENTIAL
EQUATIONS
*
158
5.2.1
MATHEMATICAL
DESCRIPTION
OF
IMPLICIT
DIFFERENTIAL
EQUATIONS
*
159
5.2.2
CONSISTENT
INITIAL
VALUE
TRANSFORMATION
*
160
5.2.3
DIRECT
SOLUTION
OF
IMPLICIT
DIFFERENTIAL
EQUATIONS
*
163
5.2.4
IMPLICIT
DIFFERENTIAL
EQUATIONS
WITH
MULTIPLE
SOLUTIONS
*
166
5.3
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
168
5.3.1
GENERAL
FORM
OF
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
168
5.3.2
INDICES
OF
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
169
5.3.3
SEMI-EXPLICIT DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
169
5.3.4
LIMITATIONS
OF
THE
DIRECT
SOLVER
*
173
5.3.5
IMPLICIT
SOLVERS
FOR
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
175
5.3.6
INDEX
REDUCTION
FOR
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
180
5.4
SWITCHED
DIFFERENTIAL
EQUATIONS
*
183
5.4.1 LINEAR
SWITCHED
DIFFERENTIAL
EQUATIONS
*
183
5.4.2 ZERO-CROSSING
DETECTION
AND
EVENT
HANDLING
*
185
5.4.3
NONLINEAR
SWITCHED
DIFFERENTIAL
EQUATIONS
*
188
5.4.4
DISCONTINUOUS
DIFFERENTIAL
EQUATIONS
*
190
5.5
LINEAR
STOCHASTIC
DIFFERENTIAL
EQUATIONS
*
191
X
*
CONTENTS
5.5.1
TRANSFER
FUNCTION
MODEL
FOR
LINEAR
STOCHASTIC
DIFFERENTIAL
EQUATIONS
*
192
5.5.2
5.5.3
5.6
ERRONEOUS
METHODS
IN
CONTINUOUS
STOCHASTIC
SYSTEM
SIMULATION
*
193
DISCRETIZING
STOCHASTIC
LINEAR
SYSTEMS
*
195
EXERCISES
*
199
6
6.1
DELAY
DIFFERENTIAL
EQUATIONS
*
205
NUMERICAL
SOLUTIONS
OF
DELAY
DIFFERENTIAL
EQUATIONS
WITH
CONSTANT
DELAYS
-----
205
6.1.1
6.1.2
6.1.3
6.2
6.2.1
6.2.2
6.2.3
6.2.4
6.3
6.3.1
6.3.2
6.4
6.5
ORDINARY
AND
DELAY
DIFFERENTIAL
EQUATIONS
*
205
DELAY
DIFFERENTIAL
EQUATION
WITH
ZERO
HISTORY
FUNCTIONS
*
207
NONZERO
HISTORY
FUNCTIONS
*
212
DIFFERENTIAL
EQUATIONS
WITH
VARIABLE
DELAYS
*
214
VARIABLE
DELAY MODELS
*
215
TIME-DEPENDENT
DELAYS
*
215
STATE-DEPENDENT
DELAYS
*
219
DELAY
DIFFERENTIAL
EQUATIONS
WITH
GENERALIZED
DELAYS
*
221
NEUTRAL-TYPE
DELAY
DIFFERENTIAL
EQUATIONS
*
222
NEUTRAL-TYPE
EQUATIONS
*
223
NEUTRAL-TYPE
DIFFERENTIAL
EQUATIONS
WITH
VARIABLE
DELAYS
*
226
VOLTERRA
DIFFERENTIAL
EQUATIONS
WITH
DELAYS
*
228
EXERCISES
*
229
7
7.1
7.1.1
PROPERTIES
AND
BEHAVIORS
OF
ORDINARY
DIFFERENTIAL
EQUATIONS
*
233
STABILITY
OF
DIFFERENTIAL
EQUATIONS
*
233
STABILITY
OF
LINEAR
DIFFERENTIAL
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
*
233
7.1.2
7.1.3
7.1.4
7.1.5
7.1.6
ROUTH-HURWITZ
STABILITY
CRITERION
*
236
LYAPUNOV
FUNCTION
AND
LYAPUNOV
STABILITY
*
239
AUTONOMOUS
CONVERSION
OF
TIME-VARYING
DIFFERENTIAL
EQUATIONS
*
240
STABILITY
ASSESSMENT
OF
NONLINEAR
SYSTEMS
BY
EXAMPLES
*
241
STABILITY
ASSESSMENT
OF
COMPLICATED
SYSTEMS
WITH
SIMULATION
METHODS
-----
243
7.2
7.2.1
7.2.2
7.2.3
7.2.4
7.3
7.3.1
7.3.2
7.3.3
SPECIAL
BEHAVIORS
OF
DIFFERENTIAL
EQUATIONS
*
246
LIMIT
CYCLES
*
246
PERIODIC
SOLUTIONS
*
251
CHAOS
AND
ATTRACTORS
*
254
POINCARE
MAPPING
*
259
LINEARIZATION
APPROXIMATION
OF
DIFFERENTIAL
EQUATIONS
*
261
EQUILIBRIUM
POINTS
-----
261
LINEARIZATION
OF
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
265
PROPERTIES
OF
EQUILIBRIA
*
269
CONTENTS
*
XI
7.4
7.5
BIFURCATION
OF
DIFFERENTIAL
EQUATIONS
*
269
EXERCISES
*
270
8
8.1
8.1.1
8.1.2
FRACTIONAL-ORDER
DIFFERENTIAL
EQUATIONS
*
273
DEFINITIONS
AND
NUMERICAL COMPUTATION
IN
FRACTIONAL
CALCULUS
*
273
DEFINITIONS
OF
FRACTIONAL
CALCULUS
*
274
RELATIONSHIPS
AND
PROPERTIES
OF
DIFFERENT
FRACTIONAL
CALCULUS
DEFINITIONS
*
275
8.1.3
8.1.4
8.2
NUMERICAL
COMPUTATION
FOR
GRUNWALD-LETNIKOV
DERIVATIVES
*
277
NUMERICAL
COMPUTATION
FOR
CAPUTO
DERIVATIVES
*
277
ANALYTICAL
SOLUTION
OF
LINEAR
COMMENSURATE-ORDER
DIFFERENTIAL
EQUATIONS
*
279
8.2.1
8.2.2
8.2.3
8.2.4
8.3
MITTAG-LEFFLER
FUNCTIONS
*
279
COMMENSURATE-ORDER
LINEAR
DIFFERENTIAL
EQUATIONS
*
280
AN
IMPORTANT
LAPLACE
TRANSFORM
FORMULA
*
281
PARTIAL
FRACTION
EXPANSION-BASED
ANALYTICAL
APPROACH
*
282
NUMERICAL
SOLUTIONS
OF
LINEAR
FRACTIONAL-ORDER
DIFFERENTIAL
EQUATIONS
WITH
CONSTANT
COEFFICIENTS
*
287
8.3.1
8.3.2
8.3.3
8.3.4
8.3.5
8.4
8.4.1
8.4.2
8.4.3
8.5
A
CLOSED-FORM
SOLUTION
*
287
RIEMANN-LIOUVILLE
DIFFERENTIAL
EQUATIONS
*
289
CAPUTO
DIFFERENTIAL
EQUATIONS
*
291
COMPUTING
EQUIVALENT
INITIAL
VALUES
*
294
HIGH
PRECISION
ALGORITHMS
*
297
SOLUTION
OF
NONLINEAR
FRACTIONAL-ORDER
DIFFERENTIAL
EQUATIONS
*
300
PREDICTOR
METHOD
*
300
CORRECTOR
METHOD
*
304
MATRIX
METHOD
FOR
IMPLICIT
CAPUTO
DIFFERENTIAL
EQUATIONS
*
305
EXERCISES
*
308
9
9.1
9.1.1
9.1.2
9.2
BLOCK
DIAGRAM
SOLUTIONS
OF
ORDINARY
DIFFERENTIAL
EQUATIONS
*
311
SIMULINK
ESSENTIALS
*
312
AN
INTRODUCTION
TO
SIMULINK
*
312
RELEVANT
BLOCKS
IN
SIMULINK
*
312
BLOCK
DIAGRAM
MODELING
METHODOLOGIES
IN
DIFFERENTIAL
EQUATIONS
-----
314
9.2.1
9.2.2
9.2.3
9.2.4
9.3
9.3.1
9.3.2
INTEGRATOR
CHAINS
AND
KEY
SIGNAL
GENERATION
*
314
DIFFERENTIAL
EQUATION
DESCRIPTION
METHODS
*
315
SOLUTIONS
OF
DIFFERENTIAL
EQUATIONS
*
318
ALGORITHMS
AND
PARAMETER
SETTINGS
*
319
MODELING
EXAMPLES
OF
DIFFERENTIAL
EQUATIONS
*
321
SIMPLE
DIFFERENTIAL
EQUATIONS
*
321
DIFFERENTIAL-ALGEBRAIC
EQUATIONS
*
325
XII
*
CONTENTS
9.3.3
SWITCHED
DIFFERENTIAL
EQUATIONS
*
327
9.3.4
DISCONTINUOUS
DIFFERENTIAL
EQUATIONS
*
330
9.3.5
DELAY
DIFFERENTIAL
EQUATIONS
*
330
9.3.6
DELAY
DIFFERENTIAL
EQUATIONS
WITH
NONZERO
HISTORY
FUNCTIONS
*
333
9.3.7
STOCHASTIC
DIFFERENTIAL
EQUATIONS
*
334
9.4
SIMULINK
MODELING
OF
FRACTIONAL-ORDER
DIFFERENTIAL
EQUATIONS
*
336
9.4.1
FRACTIONAL-ORDER
OPERATOR
BLOCK
*
337
9.4.2
MODELING
AND
SOLUTION
OF
RIEMANN-LIOUVILLE
DIFFERENTIAL
EQUATIONS
*
339
9.4.3
BLOCK
FOR
CAPUTO
DERIVATIVES
*
341
9.4.4
MODELING
AND
SOLVING
OF
CAPUTO
DIFFERENTIAL
EQUATIONS
*
341
9.4.5
FRACTIONAL-ORDER
DELAY
DIFFERENTIAL
EQUATIONS
*
344
9.5
EXERCISES
*
346
10
BOUNDARY
VALUE
PROBLEMS
FOR
ORDINARY
DIFFERENTIAL
EQUATIONS
*
349
10.1
STANDARD
BOUNDARY
VALUE
PROBLEMS
*
349
10.2
SHOOTING
METHODS
IN
TWO-POINT
BOUNDARY
VALUE
PROBLEMS
FOR
SECOND-ORDER
DIFFERENTIAL
EQUATIONS
*
350
10.2.1
SHOOTING
ALGORITHMS
FOR
LINEAR
TIME-VARYING
DIFFERENTIAL
EQUATIONS
*
351
10.2.2
FINITE
DIFFERENCE
ALGORITHM
FOR
LINEAR
DIFFERENTIAL
EQUATIONS
*
354
10.2.3
SHOOTING
ALGORITHMS
FOR
NONLINEAR
DIFFERENTIAL
EQUATIONS
*
357
10.3
TWO-POINT
BOUNDARY
VALUE
PROBLEMS
FOR
HIGH-ORDER
DIFFERENTIAL
EQUATIONS
*
360
10.3.1
DIRECT
SOLVER
IN
MATLAB
*
361
10.3.2
SOLUTION
OF
SIMPLE
BOUNDARY
VALUE
PROBLEMS
*
362
10.3.3
DESCRIPTIONS
OF
COMPLICATED
BOUNDARY
CONDITIONS
*
366
10.3.4
BOUNDARY
VALUE
PROBLEMS
WITH
UNDETERMINED
COEFFICIENTS
*
368
10.3.5
BOUNDARY
VALUE
PROBLEMS
WITH
SEMI-INFINITE
INTERVALS
*
370
10.3.6
DIFFERENTIAL
EQUATIONS
WITH
FLOATING
BOUNDARY
VALUES
*
372
10.3.7
BOUNDARY
VALUE
PROBLEMS
OF
INTEGRO-DIFFERENTIAL
EQUATIONS
*
373
10.4
OPTIMIZATION-BASED
BOUNDARY
VALUE
PROBLEM
SOLUTIONS
*
374
10.4.1
ILLUSTRATIVE
EXAMPLE
TO
SIMPLE
BOUNDARY
VALUE
PROBLEMS
*
375
10.4.2
BOUNDARY
VALUE
PROBLEMS
FOR
IMPLICIT
DIFFERENTIAL
EQUATIONS
*
376
10.4.3
BOUNDARY
VALUE
PROBLEMS
FOR
DELAY
DIFFERENTIAL
EQUATIONS
*
379
10.4.4
MULTIPOINT
BOUNDARY
VALUE
PROBLEMS
*
381
10.4.5
FLOATING
BOUNDARY
VALUE
PROBLEMS
REVISITED
*
383
10.4.6
BOUNDARY
VALUE
PROBLEMS
FOR
BLOCK
DIAGRAMS
*
384
10.4.7
BOUNDARY
VALUE
PROBLEMS
FOR
FRACTIONAL-ORDER
DIFFERENTIAL
EQUATIONS
*
386
10.5
EXERCISES
------
387
CONTENTS
*
XIII
11
PARTIAL
DIFFERENTIAL
EQUATIONS
*
391
11.1
NUMERICAL
SOLUTIONS
OF
DIFFUSION
EQUATIONS
*
392
11.1.1
MATHEMATICAL
FORM
AND
ANALYTICAL
SOLUTIONS
OF
ONE-DIMENSIONAL
DIFFUSION
EQUATIONS
*
392
11.1.2
DISCRETIZING
DIFFUSION
EQUATIONS
-----
393
11.1.3
INHOMOGENEOUS
DIFFUSION
EQUATIONS
*
397
11.1.4
MULTIDIMENSIONAL
DIFFUSION
EQUATIONS
*
399
11.2
SEVERAL
SPECIAL
FORMS
OF
PARTIAL
DIFFERENTIAL
EQUATIONS
*
399
11.2.1
CLASSIFICATION
OF
PARTIAL
DIFFERENTIAL
EQUATIONS
*
400
11.2.2
EIGENVALUE-TYPE
PARTIAL
DIFFERENTIAL
EQUATIONS
*
401
11.2.3
CLASSIFICATION
OF
BOUNDARY
CONDITIONS
*
402
11.3
USER
INTERFACE
OF
TYPICAL
TWO-DIMENSIONAL
PARTIAL
DIFFERENTIAL
EQUATIONS
*
402
11.3.1
AN
INTRODUCTION
OF
THE
USER
INTERFACE
*
402
11.3.2
GEOMETRIC
REGION
DESIGN
*
404
11.3.3
BOUNDARY
CONDITION
DESCRIPTION
*
405
11.3.4
EXAMPLES
OF
PARTIAL
DIFFERENTIAL
EQUATION
SOLUTIONS
*
406
11.3.5
OTHER
SOLUTION
DISPLAY
METHODS
*
407
11.3.6
PARTIAL
DIFFERENTIAL
EQUATIONS
WITH
FUNCTIONAL
COEFFICIENTS
*
409
11.4
SOLUTIONS
OF
PARTIAL
DIFFERENTIAL
EQUATIONS
*
410
11.4.1
CREATING
A
BLANK
PARTIAL
DIFFERENTIAL
EQUATION
OBJECT
*
411
11.4.2
STATEMENT
DESCRIPTION
OF
GEOMETRIC
REGIONS
*
411
11.4.3
BOUNDARY
AND
INITIAL
CONDITION
DESCRIPTIONS
*
415
11.4.4
PARTIAL
DIFFERENTIAL
EQUATIONS
DESCRIPTIONS
*
415
11.4.5
NUMERICAL
SOLUTIONS
OF
PARTIAL
DIFFERENTIAL
EQUATIONS
*
417
11.5
EXERCISES
*
423
BIBLIOGRAPHY
*
425
MATLAB
FUNCTION
INDEX
*
429
INDEX
-----
433 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Xue, Dingyu |
| author_GND | (DE-588)1098160967 |
| author_facet | Xue, Dingyu |
| author_role | aut |
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| building | Verbundindex |
| bvnumber | BV046719736 |
| classification_rvk | ST 601 SK 500 |
| ctrlnum | (OCoLC)1125818660 (DE-599)DNB1197821368 |
| dewey-full | 515.350285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.350285 |
| dewey-search | 515.350285 |
| dewey-sort | 3515.350285 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV046719736 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:33:15Z |
| indexdate | 2024-07-10T08:51:59Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110675245 3110675242 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032129977 |
| oclc_num | 1125818660 |
| open_access_boolean | |
| owner | DE-634 DE-83 DE-703 DE-706 DE-19 DE-BY-UBM DE-20 DE-11 |
| owner_facet | DE-634 DE-83 DE-703 DE-706 DE-19 DE-BY-UBM DE-20 DE-11 |
| physical | XIII, 438 Seiten Illustrationen, Diagramme |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter STEM |
| spelling | Xue, Dingyu Verfasser (DE-588)1098160967 aut Differential equation solutions with MATLAB Dingyü Xue Berlin ; Boston De Gruyter [2020] [Beijing] Tsinghua University Press [2020] © 2020 XIII, 438 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier De Gruyter STEM Differentialgleichung (DE-588)4012249-9 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s MATLAB (DE-588)4329066-8 s DE-604 Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-067525-2 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-067531-3 B:DE-101 application/pdf https://d-nb.info/1197821368/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032129977&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Xue, Dingyu Differential equation solutions with MATLAB Differentialgleichung (DE-588)4012249-9 gnd MATLAB (DE-588)4329066-8 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4329066-8 |
| title | Differential equation solutions with MATLAB |
| title_auth | Differential equation solutions with MATLAB |
| title_exact_search | Differential equation solutions with MATLAB |
| title_exact_search_txtP | Differential equation solutions with MATLAB |
| title_full | Differential equation solutions with MATLAB Dingyü Xue |
| title_fullStr | Differential equation solutions with MATLAB Dingyü Xue |
| title_full_unstemmed | Differential equation solutions with MATLAB Dingyü Xue |
| title_short | Differential equation solutions with MATLAB |
| title_sort | differential equation solutions with matlab |
| topic | Differentialgleichung (DE-588)4012249-9 gnd MATLAB (DE-588)4329066-8 gnd |
| topic_facet | Differentialgleichung MATLAB |
| url | https://d-nb.info/1197821368/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032129977&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT xuedingyu differentialequationsolutionswithmatlab AT walterdegruytergmbhcokg differentialequationsolutionswithmatlab |