The purpose of this paper is to propose a non‐polynomial spline‐based method to obtain numerical solutions of a dissipative wave equation. Applying the Von Neumann stability analysis, the developed method is shown to be conditionally stable for given values of specified parameters. A numerical example is given to illustrate the applicability and the accuracy of the proposed method. The obtained numerical results reveal that our proposed method maintains good accuracy.
A non‐polynomial spline is proposed based on the dissipative wave equation, which gives nonlinear system of algebraic equations; by solving these equations, the numerical solution is found.
It is found that the method gives more accurate numerical results for such nonlinear partial differential equations. The stability is good.
Any nonlinear or linear partial differential equation can be solved by such method.
We compare between the numerical and analytic solutions of the dissipative wave equation, also the error norms which were small.
This paper presents a new method to solve such problems.
