Numerical solution of two point boundary value problems by wavelet Galerkin method

Abstract

In this paper, the Legendre wavelet operational matrix of integration is used to solve two point boundary value problems, in which the coefficients of the ordinary differential equation are real valued functions whose inner product with Legendre wavelet basis functions must exist. The method and convergence analysis of the Legendre wavelet is discussed. This method is applied to solve three boundary value and two moving boundary problems. In boundary value problems, we have studied the effects of condition number, elapse time and relative error on Legendre wavelet. It has been observed that the error decreases as the number of wavelet basis function increases. The condition number of square matrix of matrix equation decreases as Legendre wavelet basis function increases. The Legendre wavelet Galerkin method provides better results in lesser time, in comparison of other methods. In case of moving boundary problems the root mean square error (RMSE) for dimensionless temperature, position of moving interface and its generalized time rate are evaluated. It has been observed that the error increases as Stefan number increases.