NUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE

Authors

Department of Mathematics, Iran University of Science and Technology, Iran, Islamic Republic of

Abstract

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.

Keywords