University of Guilan Journal of Mathematical Modeling 2345-394X 14 2 2026 05 01 A robust fitted finite difference method for semi-linear two-parameter singularly perturbed PDEs 379 405 9196 10.22124/jmm.2025.30916.2776 EN Mekashaw Ali Mohye Department of Mathematics, College of Natural and Computational Science, Wolkite University, Wolkite, Ethiopia Justin B. Munyakazi Department of Mathematics and Applied Mathematics University of Western Cape Tekle Gemechu Dinka Department of Applied Mathematics Adama Science and Technology University Yusuf Hussen Haji Department of Mathematics, Arsi University, Asela, Ethiopia Abe NUra Ware Department of Mathematics, Arsi University, Asela, Ethiopia Jemal Muhammed Ahmed Department of Mathematics, Oda Bultum University, Chiro, Ethiopia Journal Article 2025 06 09 In this article, a new numerical approach is developed for nonlinear two-parameter singularly perturbed initial-boundary value problems. The implicit backward Euler discretization for the time derivative and the fitted operator technique in the spatial domain are employed. Newton's quasilinearization technique is applied to the nonlinear terms. An investigation of parameter-uniform error estimates shows that the developed approach is first-order accurate in both time and space. However, a temporal mesh refinement technique is introduced to improve the order of accuracy to two. Two examples are provided and implemented in Python to validate the applicability of the method, and the results are displayed in tables and graphs. https://jmm.guilan.ac.ir/article_9196_a1da3bcb9a2e740a13facab78cc434d7.pdf