Biorthogonal wavelet-based multigrid and full approximation scheme for the numerical solution of parabolic partial differential equations

Abstract

This paper presents biorthogonal wavelet-based multigrid (BWMG) and full approximation scheme (FAS) for the numerical solution of parabolic partial differential equations (PPDEs), which are working horse behind many commercial applications like finger print image compression. Performance of the proposed schemes is better than the existing ones in terms of super convergence with less computational time. Some of the test problems are taken to demonstrate the applicability and validity of the method.

Higher Order Haar Wavelet Method for Solving Differential Equations

“…Let us consider first the n-th order ordinary differential Eq. (8). According to the the Haar wavelet expansion is expressed as.…”

“…The Legendre wavelets are utilized to solve fractional differential equations in [1][2][3][4] and integro-differential equations in [5,6]. In [7,8], the Daubechies wavelet based approximation algorithms are derived to solve ordinary and partial differential equations. In [9], the Lucas wavelets are combined with Legendre-Gauss quadrature for solving fractional Fredholm-Volterra integrodifferential equations.…”