Novel techniques for solving Goursat partial differential equations in the linear and nonlinear regime

Abstract

The Goursat problem, which is related to hyperbolic partial differential equations, occurs in a variety of branches of physics and engineering. We studied the solution of the Goursat partial differential equation utilizing the reduced differential transform (RDT) and Adomian decomposition (AD) techniques in this inquiry. The problem's analytical solution is found in series form, which converges to exact solutions. The approaches' reliability and efficiency were evaluated using the Goursat problems (linear and non-linear). Additionally, the accuracy of the findings obtained demonstrates the reduced differential approach's superiority over the Adomian decomposition method and other numerical methods previously applied to the Goursat problem.