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Optimization of Finite Difference Method with Multiwavelet Bases

  • Eratt P. Sumesh
  • Elizabeth Elias
Part of the Communications in Computer and Information Science book series (CCIS, volume 40)

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 Schrödinger equation and Burgers’ equation.

Keywords

Finite Difference Method multiwavelets partial differential equation discretization grid size iteration 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Eratt P. Sumesh
    • 1
  • Elizabeth Elias
    • 2
  1. 1.Department of Electronics and Communication EngineeringAmrita School of Engineering, EttimadaiCoimbatoreIndia
  2. 2.Department of Electronics and Communication EngineeringNational Institute of TechnologyCalicutIndia

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