Robust Numerical Approach for Solving Robin Boundary Value Problems
نویسندگان
1 Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt//Department of Mathematics, Faculty of Science, Galala University, Suez, 43511, Egypt//Scientific Research School of Egypt (SRSEG)
2 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt
doi
10.22052/ijmc.2025.256851.2008چکیده
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.
