Numerical solution of one dimensional heat equation using Radial basis functions

Abstract

In this thesis, inverse Multiquadric Radial basis functions for solving 1D heat equation is presented. First, the solution domain is discretized and the derivative involving the spatial variable is replaced by the sum of the weighting coefficients times functional values at each grid points along the spatial variable. Then, the resulting first order linear ordinary differential equation is solved by ode 45. To validate the applicability of the present method, one model example is considered and solved for different shape parameter ‘c’. Numerical results are presented in tables in terms of root mean square   2 E , maximum absolute error () E  and condition number of the system matrix. The numerical results presented in tables and graphs show that, the present method approximates the exact solution very well and is superior over the method presented by Dehghan and Tatari, 2010.