Numerical Solution of One-Dimensional Heat and Wave Equation by Non-Polynomial Quintic Spline

This paper present a novel numerical algorithm for the linear one- dimensional heat and wave equation. In this method, a nite dierence approach had been used to discrete the time derivative while cubic spline is applied as an interpolation function in the space dimension. We discuss the accuracy of the method by expanding the equation based on Taylor series and minimize the error. The proposed method has eighth-order accuracy in space and fourth-order accuracy in time variables. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is ecient to use. Numerical examples are given to show the applicability and eciency of the method.