Explicit and Implicit Numerical Investigationof One-Dimensional Heat Equation Based on Spline Collocation and Thomas Algorithm

Abstract

In this paper, the explicit and implicit techniques are adopted to obtain the numerical solution of one-dimensional heat equation (parabolic linear partial differential equation) with the help of cubic spline technique. Spline provides continuous solution and the set of simultaneous equations obtained in explicit as well as implicit scheme can be solved by Thomas algorithm form tridiagonal dominant matrix. The efficiency and accuracy of the present scheme is justified through five numerical examples and the results are also compared with the analytical results and others in terms of error and error norms and . Stability analysis is performed using Von-Neuman approach and truncation error of both the schemes are performed and found to be convergence of order.