An Effective Computational Technique for Solving Nonlinear Boundary Value Problems Arising in Various Physical Phenomena

ABSTRACT This paper introduces a precise computational approach utilizing domain decomposition to solve second‐order nonlinear boundary value problems (BVPs) that model various physical phenomena, including the Bratu problem. The approach combines quasilinearization and the Picard iteration technique in an effective domain decomposition strategy. Through quasilinearization, the problem is simplified into a series of linear equations, which are then solved to yield iterative solutions. The study also examines sufficient convergence properties. This approach provides highly accurate results for Bratu's problem near the critical value. The paper presents several numerical simulations to showcase the method's applicability. Furthermore, the new technique has been successfully applied to a broad range of BVPs, including those with nonlinear boundary conditions and nonlinear systems, demonstrating its effectiveness and versatility across diverse problem types.