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

In this paper, a numerical method based on non-polynomial spline functions is presented to solve the one-dimensional heat equation. The new method is unconditionally stable. The accuracy order of the new method is of O(k5+h4),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.