A Non-polynomial Spline Method for Solving the One-Dimensional Heat Equation

Abstract

In this paper, a numerical method based on nonpolynomial spline functions is presented to solve the onedimensional heat equation. The new method is unconditionally stable. The accuracy order of the new method is of O(k 5 + h 4 ), where k and h denote the mesh parameters for t and x, respectively. The accuracy of the present method is much higher than previous known methods.