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

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