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Numerical Solution of Nonlinear Klein-Gordon Equation Using Polynomial Wavelets

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Intelligent Mathematics II: Applied Mathematics and Approximation Theory

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 441))

Abstract

The main aim of this paper is to apply the polynomial wavelets for the numerical solution of nonlinear Klein-Gordon equation. Polynomial scaling and wavelet functions are rarely used in the contexts of numerical computation. A numerical technique for the solution of nonlinear Klein-Gordon equation is presented. Our approach consists of finite difference formula combined with the collocation method, which uses the polynomial wavelets. Using the operational matrix of derivative, we reduce the problem to a set of algebraic equations by expanding the approximate solution in terms of polynomial wavelets with unknown coefficients. An estimation of error bound for this method is investigated. Some illustrative examples are included to demonstrate the validity and applicability of the approach.

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Authors and Affiliations

  1. School of Mathematics, Iran University of Science and Technology, Tehran, Iran

    Jalil Rashidinia & Mahmood Jokar

Authors
  1. Jalil Rashidinia
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  2. Mahmood Jokar
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Correspondence to Mahmood Jokar .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee, USA

    George A. Anastassiou

  2. Department of Mathematics, TOBB Economics and Technology University, Ankara, Turkey

    Oktay Duman

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Rashidinia, J., Jokar, M. (2016). Numerical Solution of Nonlinear Klein-Gordon Equation Using Polynomial Wavelets. In: Anastassiou, G., Duman, O. (eds) Intelligent Mathematics II: Applied Mathematics and Approximation Theory. Advances in Intelligent Systems and Computing, vol 441. Springer, Cham. https://doi.org/10.1007/978-3-319-30322-2_14

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  • DOI: https://doi.org/10.1007/978-3-319-30322-2_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30320-8

  • Online ISBN: 978-3-319-30322-2

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