Numerical solution of parabolic partial differential equations using adaptive gird Haar wavelet collocation method

Abstract

In this paper, we applied the adaptive grid Haar wavelet collocation method (AGH-WCM) for the numerical solution of parabolic partial differential equations (PDEs). The approach of AGHWCM for the numerical solution of parabolic PDEs is mentioned, the obtained numerical results, error analysis are presented in figures and tables. This shows that, the AGHWCM gives better accuracy than the HWCM and FDM. Some of the test problems are taken for demonstrating the validity and applicability of the AGHWCM.

A Comparative Study on Haar Wavelet and Hosaya Polynomial for the numerical solution of Fredholm integral equations

“…Shiralashetti et al [13][14][15][16]18] applied for the numerical solution of Klein?Gordan equations, multi-term fractional differential equations, singular initial value problems,nonlinear Fredholm integral equations, Riccati and Fractional Riccati Differential Equations. Shiralashetti et al [17] have introduced the adaptive gird Haar wavelet collocation method for the numerical solution of parabolic partial differential equations.…”

Numerical Solution of Nonlinear Volterra-Fredholm Integral Equations Using Haar Wavelet Collocation Method

“…Shiralashetti et al [24][25][26][27] applied for the numerical solution of KleinGordan equations, multi-term fractional differential equations, singular initial value problems and Riccati and Fractional Riccati Differential Equations. Shiralashetti et al [28] have introduced the adaptive gird Haar wavelet collocation method for the numerical solution of parabolic partial differential equations. Also, Haar wavelet method is applied for different kind of integral equations, which among Lepik et al [29][30][31][32] presented the solution for differential and integral equations.…”