A Novel Computational Algorithm for Efficiently Solving Partial Differential Equations

This study introduces a novel approximate analytical method for solving nonlinear partial differential equations, both homogeneous and non-homogeneous.The proposed approach is based on the expansion of solutions using the Taylor series, and a systematic framework is developed for its implementation across a broad class of equations.The convergence behavior of the approximate solution toward the exact solution is analyzed, and the efficiency of the method is demonstrated through numerical examples and graphical illustrations.The results indicate that the proposed method is a promising and effective tool due to its simplicity and high accuracy when compared with traditional techniques.