University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 17 1 2026 03 01 Robust Numerical Approach for Solving Robin Boundary Value Problems 77 94 115431 10.22052/ijmc.2025.256851.2008 EN Ahmed Gamal Atta Department of Mathematics‎, ‎Faculty of Education‎, ‎Ain Shams University‎, ‎Roxy‎, ‎Cairo 11341‎, ‎Egypt Sameh H. Basha 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) Journal Article 2025 05 13 ‎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. https://ijmc.kashanu.ac.ir/article_115431_76a80efccde54a19152d9b933fcc377e.pdf