Yisa, Babatunde MorufuTijani, Saadatu Abubakar2026-04-152026-04-152026-04-01Yisa, B. M. & Tijani, S. A. (2026): Analytical Solutions of Nonlinear Initial-Boundary Value Problems, Centrepoint Journal (Science Edition), 30 (1), 59 – 75.https://uilspace.unilorin.edu.ng/handle/123456789/17190This work presents solutions to initial-boundary value problems that are generally nonlinearexploringTaylor’s theorem in a decomposition technic. Not until few decades back, real world phenomena in many fields of human endeavours were modelled into initial and boundary value problems. Due to identified deficiencies in doing that, initial-boundary value equations are used to achieve the aim.The problems are mostly nonlinear. Solution to such category of problems mostly defies the use of the established analytical methods. Most researchers employ numerical approaches that result in approximate solutions. The present approach uses Taylor’s theorem alongside Adomian decomposition method. The nonlinear aspect is treated by decomposing it into polynomials, while the resulting unknown terms are evaluated through Taylor’s expansion. The method is applied to eight problems in literature, all of which give exact solution. Mathematica 13.3 is employed for the simulations.enArticle