Abstract
Non-linear differential equations play a central role in modeling complex phenomena in physical, chemical, and biological sciences. Exact analytical solutions are rarely obtainable due to strong nonlinearities and complex boundary conditions. In this work, approximate analytical and semi-analytical methods are employed to construct accurate solutions for representative non-linear boundary value and reaction diffusion problems. The methodology is based on Homotopy-type approaches, decomposition techniques, and recently developed semi-analytical formulations. The effectiveness of the proposed framework is demonstrated through applications in physical boundary value problems, chemical reaction–diffusion systems, and biological biosensor models. The results show excellent agreement with numerical solutions reported in the literature, confirming the accuracy, convergence, and computational efficiency of the methods.
Keywords
Approximate analytical methods, Non-linear differential equations, Initial value problems, Boundary value problems, Reactiondiffusion equation, Magnetohydrodynamic (MHD)