Numerical solution of boundary value problems by using an optimized two-step block method
This paper aims at the application of an optimized two-step hybrid block method for solving boundary value problems with different types of boundary conditions. The proposed approach produces simultaneously approximations at all the grid points after solving an algebraic system of equations. The fin...
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| Veröffentlicht in: | Numerical algorithms 2020-05, Vol.84 (1), p.229-251 |
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| creator | Ramos, Higinio Rufai, M. A. |
| description | This paper aims at the application of an optimized two-step hybrid block method for solving boundary value problems with different types of boundary conditions. The proposed approach produces simultaneously approximations at all the grid points after solving an algebraic system of equations. The final approximate solution is obtained through a homotopy-type strategy which is used in order to get starting values for Newton’s method. The convergence analysis shows that the proposed method has at least fifth order of convergence. Some numerical experiments such as Bratu’s problem, singularly perturbed, and nonlinear system of BVPs are presented to illustrate the better performance of the proposed approach in comparison with other methods available in the recent literature. |
| doi_str_mv | 10.1007/s11075-019-00753-3 |
| format | Article |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Algebra Algorithms Approximation Boundary conditions Boundary value problems Computer Science Convergence Methods Nonlinear systems Numeric Computing Numerical Analysis Ordinary differential equations Original Paper Theory of Computation |
| title | Numerical solution of boundary value problems by using an optimized two-step block method |
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