Discontinuous Legendre Wavelet Galerkin Method for Solving Lane-Emden Type Equation

Abstract

Abstract. This paper presents a new numerical approach, i.e., discontinuous Legendre wavelet Galerkin (DLWG) technique, to solve the Lane-Emden equations. This scheme incorporates Legendre wavelet into discontinuous Galerkin (DG) method, thus it has the advantages of both wavelet Galerkin (WG) method and DG technique. Specifically, the variational formulation of the equation and numerical fluxes are first derived and clearly calculated, then the Lane-Emden equations are converted into solutions to systems of equations. It is pointed that the proposed approach needs less storage space and execution time than the other methods because of the use of discontinuous elements producing lower dimensional, block-diagonal and sparse mass matrices. Furthermore, numerical experiments demonstrate the efficiency and applicability of this technique.

Combined variational iteration method with chebyshev wavelet for the solution of convection-diffusion-reaction problem

“…The problems remain still challenging task for many researchers from all around the world. Therefore, they are keenly attracted to this area of research [4][5][6].…”

“…Generally, the determination of the analytical solution for the nonlinear diffusion Equations specifically with nonlinear internal source terms is not very straightforward. Many approaches have been proposed to solve the linear and nonlinear PDEs like Adomain Decomposition Methods (ADM) [7][8][9], Homotopy Perturbation techniques [10,11], Legendre wavelet technique (LW) [5,6,[12][13][14][15][16], Haar wavelet technique [17][18][19], Chebyshev wavelet (CW) technique [20,21] and variational iteration method (VIM) [22][23][24][25]. The PDEs based problems are generally solved with known suitable boundary information, whereas the ordinary differential equations (ODEs) are generally solved as initial value problems (IVP) [1,13].…”