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.
This study introduces a novel and very accurate method for implementing
Robin boundary conditions while solving boundary value problems with
compact finite difference schemes. Most studies numerically approximate
Neumann and Robin boundary conditions with a first-order approximation,
however, this reduces the accuracy in general. Our implementation
produces highly accurate results in solving nonlinear singular boundary
value problems. Other reported results achieved utilizing various
techniques are used for comparison. Tables and graphs showing the
results are given.
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