High accuracy cubic spline finite difference approximation for the solution of one-space dimensional non-linear wave equations
In this paper, we propose a new three-level implicit nine point compact cubic spline finite difference formulation of order two in time and four in space directions, based on cubic spline approximation in x-direction and finite difference approximation in t-direction for the numerical solution of on...
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| Veröffentlicht in: | Applied mathematics and computation 2011-12, Vol.218 (8), p.4234-4244 |
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| creator | Mohanty, R.K. Gopal, Venu |
| description | In this paper, we propose a new three-level implicit nine point compact cubic spline finite difference formulation of order two in time and four in space directions, based on cubic spline approximation in
x-direction and finite difference approximation in
t-direction for the numerical solution of one-space dimensional second order non-linear hyperbolic partial differential equations. We describe the mathematical formulation procedure in details and also discuss how our formulation is able to handle wave equation in polar coordinates. The proposed method when applied to a linear hyperbolic equation is also shown to be unconditionally stable. Numerical results are provided to justify the usefulness of the proposed method. |
| doi_str_mv | 10.1016/j.amc.2011.09.054 |
| format | Article |
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x-direction and finite difference approximation in
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x-direction and finite difference approximation in
t-direction for the numerical solution of one-space dimensional second order non-linear hyperbolic partial differential equations. We describe the mathematical formulation procedure in details and also discuss how our formulation is able to handle wave equation in polar coordinates. The proposed method when applied to a linear hyperbolic equation is also shown to be unconditionally stable. Numerical results are provided to justify the usefulness of the proposed method.</description><subject>Approximation</subject><subject>Cubic spline approximation</subject><subject>Exact sciences and technology</subject><subject>Handles</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Maximum absolute errors</subject><subject>Non-linear hyperbolic equation</subject><subject>Nonlinearity</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Partial differential equations</subject><subject>Partial differential equations, boundary value problems</subject><subject>Partial differential equations, initial value problems and time-dependant initial-boundary value problems</subject><subject>Polar coordinates</subject><subject>Sciences and techniques of general use</subject><subject>Splines</subject><subject>Telegraphic equation</subject><subject>Vander Pol equation</subject><subject>Wave equation in polar coordinates</subject><subject>Wave equations</subject><issn>0096-3003</issn><issn>1873-5649</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kMFu1DAQhi0EEkvhAbj5gsQlYRxvkrU4oYpSpEpc4GxNJmPqVdZO7aTQC8-O0604Ih8sjb7_t-cT4q2CWoHqPhxrPFHdgFI1mBra_TOxU4deV223N8_FDsB0lQbQL8WrnI8A0HdqvxN_rv3PW4lEa0J6kLQOnmSeJx9YOh_8wnL0znHiQCxxnlP87U-4-Biki0kutyxznNbHQXQyBq7yjLTFThxyGeMkQwzVVolJ_sJ7lny3Plbk1-KFwynzm6f7Qvy4-vz98rq6-fbl6-Wnm4p0B0s19GTMCMZoZ9C4FroRzYCHPfVubGgYDn2rtcGuGUk5ajrWPRoalYMRGuP0hXh_7i3_v1s5L_bkM_E0YeC4ZlscwqE35RRUnVFKMefEzs6pbJweCrRxnT3a4tpuri0YW1yXzLunesyEk0sYyOd_wabVSqtm4z6eOS673ntONpPfzI4-MS12jP4_r_wFhkuXNA</recordid><startdate>20111215</startdate><enddate>20111215</enddate><creator>Mohanty, R.K.</creator><creator>Gopal, Venu</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20111215</creationdate><title>High accuracy cubic spline finite difference approximation for the solution of one-space dimensional non-linear wave equations</title><author>Mohanty, R.K. ; Gopal, Venu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c360t-b7c99d0993f9a9f506da9ba84c7fd2cbb875339a62dc1fc26e37a9cd1f0d029f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Approximation</topic><topic>Cubic spline approximation</topic><topic>Exact sciences and technology</topic><topic>Handles</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Maximum absolute errors</topic><topic>Non-linear hyperbolic equation</topic><topic>Nonlinearity</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Partial differential equations</topic><topic>Partial differential equations, boundary value problems</topic><topic>Partial differential equations, initial value problems and time-dependant initial-boundary value problems</topic><topic>Polar coordinates</topic><topic>Sciences and techniques of general use</topic><topic>Splines</topic><topic>Telegraphic equation</topic><topic>Vander Pol equation</topic><topic>Wave equation in polar coordinates</topic><topic>Wave equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mohanty, R.K.</creatorcontrib><creatorcontrib>Gopal, Venu</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Applied mathematics and computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mohanty, R.K.</au><au>Gopal, Venu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>High accuracy cubic spline finite difference approximation for the solution of one-space dimensional non-linear wave equations</atitle><jtitle>Applied mathematics and computation</jtitle><date>2011-12-15</date><risdate>2011</risdate><volume>218</volume><issue>8</issue><spage>4234</spage><epage>4244</epage><pages>4234-4244</pages><issn>0096-3003</issn><eissn>1873-5649</eissn><coden>AMHCBQ</coden><abstract>In this paper, we propose a new three-level implicit nine point compact cubic spline finite difference formulation of order two in time and four in space directions, based on cubic spline approximation in
x-direction and finite difference approximation in
t-direction for the numerical solution of one-space dimensional second order non-linear hyperbolic partial differential equations. We describe the mathematical formulation procedure in details and also discuss how our formulation is able to handle wave equation in polar coordinates. The proposed method when applied to a linear hyperbolic equation is also shown to be unconditionally stable. Numerical results are provided to justify the usefulness of the proposed method.</abstract><cop>Amsterdam</cop><pub>Elsevier Inc</pub><doi>10.1016/j.amc.2011.09.054</doi><tpages>11</tpages></addata></record> |
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| ispartof | Applied mathematics and computation, 2011-12, Vol.218 (8), p.4234-4244 |
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| source | Access via ScienceDirect (Elsevier) |
| subjects | Approximation Cubic spline approximation Exact sciences and technology Handles Mathematical analysis Mathematical models Mathematics Maximum absolute errors Non-linear hyperbolic equation Nonlinearity Numerical analysis Numerical analysis. Scientific computation Partial differential equations Partial differential equations, boundary value problems Partial differential equations, initial value problems and time-dependant initial-boundary value problems Polar coordinates Sciences and techniques of general use Splines Telegraphic equation Vander Pol equation Wave equation in polar coordinates Wave equations |
| title | High accuracy cubic spline finite difference approximation for the solution of one-space dimensional non-linear wave equations |
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