Implementation of New Iterative Method for Solving Nonlinear Partial Differential Problems

Abstract

Nonlinear partial differential equations (PDEs) are prevalent in various scientific and engineering fields, demanding efficient solution methods. This study focuses on the practical application and evaluation of a well-established iterative method; New Iterative Method (NIM) for solving nonlinear PDEs. The primary aim is to assess the method's performance and applicability in solving nonlinear PDEs. We present the chosen iterative method, discuss its mathematical basis, and analyze its convergence properties, accuracy, and computational efficiency. We also provide insights into practical implementations and conduct numerical experiments on diverse nonlinear PDEs. Numerical experiments across various nonlinear PDEs confirm the method's accuracy and computational efficiency, positioning it favorably compared to existing approaches. The NIM’s versatility and computational efficiency makes it a valuable tool for tackling complex problems. This innovation has the potential to greatly benefit scientific and engineering communities dealing with nonlinear PDEs, offering a promising solution for challenging real-world problems.