Paper Info
Title
Optimization of Finite Difference Method with Multiwavelet Bases
Abstract
Multiwavelet based methods are among the latest techniques to solve partial differential equations (PDEs) numerically. Finite Difference Method (FDM) - powered by its simplicity - is one of the most widely used techniques to solve PDEs numerically. But it fails to produce better result in problems where the Solution is having both sharp and smooth variations at different regions of interest. In Such cases, to achieve a given accuracy an adaptive scheme for proper grid placement is needed. In this paper we propose a method, 'Multiwavelet Optimized Finite Difference Method' (MWOFD) to overcome the drawback of FDM. In the proposed method, multiwavelet coefficients are used to place non-uniform grids adaptively. This method is highly converging and requires only less number of grids to achieve a given accuracy when contrasted with FDM. The method is demonstrated for nonlinear Schrodinger equation and Burgers' equation.
Year
DOI
Venue
2009
10.1007/978-3-642-03547-0_5
Communications in Computer and Information Science
Keywords
Field
DocType
Finite Difference Method,multiwavelets,partial differential equation discretization,grid size,iteration
Applied mathematics,Mathematical optimization,Grid size,Pattern recognition,Computer science,Finite difference coefficient,Finite difference method,Artificial intelligence,Nonlinear Schrödinger equation,Partial differential equation,Grid
Conference
Volume
ISSN
Citations 
40
1865-0929
0
PageRank 
References 
Authors
0.34
2
2
Name
Order
Citations
PageRank
Eratt P. Sumesh100.34
Elizabeth Elias216817.26