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Robust Numerical Approach for Solving Robin Boundary Value Problems
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DOI：10.22052/IJMC.2025.256851.2008.png)
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Abstract
En 中文
In this work, we introduce and develop spectral collocation techniques for solving second-order differential equations (SODEs) arising in chemical processes such as catalytic reactions, diffusion-reaction systems, and thermal conduction in reactive media, where Robin boundary conditions naturally emerge due to combined flux and concentration constraints. The proposed approach can be roughly represented as a truncated series of modified shifted fourth-kind Chebyshev polynomials (4KCPs). The unknown expansion coefficients are determined using the spectral collocation method. Collocation nodes were the shifted 4KCPs roots. The resulting nonlinear algebraic system is solved efficiently using Newton's method. We present a theorem that shows the truncation error rapidly converges with respect to the number of retained modes. The method's applicability and effectiveness are demonstrated using some numerical examples. (c) 2026 University of Kashan Press. All rights reserved
Keywords:
Fourth-kind Chebyshev polynomials
Collocation method
Second-order differential equations
Error analysis
Journal
I
IF:
1.5
Papers:
12
Citations:
0