Non-Polynomial Splines and Solving the Heat Equation

Abstract

This paper discusses the application of the polynomial, exponential and trigonometric splines of the fourth order of approximation to the construction of methods for numerically solving the heat conduction problem. The exponential splines and the trigonometric splines are used here to approximate the partial derivatives. This approach allows us to construct explicit and implicit difference schemes. The main focus of the paper is on implicit difference schemes. Numerical examples are given.