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Optimization of Finite Difference Method with Multiwavelet Bases

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Contemporary Computing (IC3 2009)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 40))

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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.

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Author information

Authors and Affiliations

  1. Department of Electronics and Communication Engineering, Amrita School of Engineering, Ettimadai, Coimbatore, India

    Eratt P. Sumesh

  2. Department of Electronics and Communication Engineering, National Institute of Technology, Calicut, Kerala, India

    Elizabeth Elias

Authors
  1. Eratt P. Sumesh
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  2. Elizabeth Elias
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Editor information

Editors and Affiliations

  1. Dept. of Computer Sciences, University of Florida, Gainesville, FL, 32611, USA

    Sanjay Ranka

  2. Laurence H. Baker Center for Bioinformatics and Biological Statistics, Iowa State University, USA

    Srinivas Aluru

  3. Grid Computing and Distributed Systems Laboratory and, NICTA Victoria Laboratory, Department of Computer Science and Software Engineering, The University of Melbourne, Australia

    Rajkumar Buyya

  4. Department of Computer Science, National Tsing Hua University, Taiwan

    Yeh-Ching Chung

  5. Computer Science, College of Engineering and Science, Louisiana Tech University, Ruston, LA, 71272, USA

    Sumeet Dua  & Vir V. Phoha  & 

  6. Department of Computer Sciences, Purdue University, W. Lafayette, IN, 47907, USA

    Ananth Grama

  7. Arizona State University, Tempe, AZ, 85281, USA

    Sandeep K. S. Gupta

  8. Computer Science and Engineering Department, Indian Institute of Technology Kharagpur, 721 302, WB, India

    Rajeev Kumar

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© 2009 Springer-Verlag Berlin Heidelberg

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Sumesh, E.P., Elias, E. (2009). Optimization of Finite Difference Method with Multiwavelet Bases. In: Ranka, S., et al. Contemporary Computing. IC3 2009. Communications in Computer and Information Science, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03547-0_5

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  • DOI: https://doi.org/10.1007/978-3-642-03547-0_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03546-3

  • Online ISBN: 978-3-642-03547-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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