Non-polynomial spline method for the solution of the dissipative wave equation

Purpose - 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. Design/methodology/approach - 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. Findings - It is found that the method gives more accurate numerical results for such nonlinear partial differential equations. The stability is good. Research limitations/implications - Any nonlinear or linear partial differential equation can be solved by such method. Practical implications - We compare between the numerical and analytic solutions of the dissipative wave equation, also the error norms which were small. Originality/value - This paper presents a new method to solve such problems.