Highly Accurate Compact Finite Difference Schemes for Two-Point Boundary Value Problems with Robin Boundary Conditions

In this study, a high-order compact finite difference method is used to solve boundary value problems with Robin boundary conditions. The norm is to use a first-order finite difference scheme to approximate Neumann and Robin boundary conditions, but that compromises the accuracy of the entire scheme...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-08, Vol.14 (8), p.1720
Main Authors: Malele, James, Dlamini, Phumlani, Simelane, Simphiwe
Format: Article
Language:English
Subjects:
Accuracy
Approximation
Boundary conditions
Boundary value problems
compact finite differences
Exact solutions
Finite difference method
quasilinearization
Robin boundary conditions
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Summary:In this study, a high-order compact finite difference method is used to solve boundary value problems with Robin boundary conditions. The norm is to use a first-order finite difference scheme to approximate Neumann and Robin boundary conditions, but that compromises the accuracy of the entire scheme. As a result, new higher-order finite difference schemes for approximating Robin boundary conditions are developed in this work. Six examples for testing the applicability and performance of the method are considered. Convergence analysis is provided, and it is consistent with the numerical results. The results are compared with the exact solutions and published results from other methods. The method produces highly accurate results, which are displayed in tables and graphs.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14081720