A computational approach to the wave equations An application of the decomposition method

A computational approach to the wave equations An application of the decomposition method Studies an analytic solution and a reliable numerical approximation of linear and non‐linear wave equations by using the Adomian decomposition method. The solution is calculated in the form of a series with easily computable components. The non‐homogeneous problem is quickly solved by observing the self‐cancelling “noise terms” where the sum of the components vanishes in the limit. Several linear or non‐linear partial differential equations are considered and their numerical approximate solutions are compared with its numerical analytic solutions by applying the Adomian decomposition method and using a computer algebraic system (MATLAB). The numerical results show the effectiveness of the method for these types of equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Kybernetes Emerald Publishing

A computational approach to the wave equations An application of the decomposition method

Kybernetes, Volume 33 (1): 18 – Jan 1, 2004

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Publisher
Emerald Publishing
Copyright
Copyright © 2004 Emerald Group Publishing Limited. All rights reserved.
ISSN
0368-492X
DOI
10.1108/03684920410514535
Publisher site
See Article on Publisher Site

Abstract

Studies an analytic solution and a reliable numerical approximation of linear and non‐linear wave equations by using the Adomian decomposition method. The solution is calculated in the form of a series with easily computable components. The non‐homogeneous problem is quickly solved by observing the self‐cancelling “noise terms” where the sum of the components vanishes in the limit. Several linear or non‐linear partial differential equations are considered and their numerical approximate solutions are compared with its numerical analytic solutions by applying the Adomian decomposition method and using a computer algebraic system (MATLAB). The numerical results show the effectiveness of the method for these types of equations.

Journal

KybernetesEmerald Publishing

Published: Jan 1, 2004

Keywords: Linear structure equation modelling; Cybernetics; Noise control; Wave properties

References

  • Convergence of Adomian's method
    Cherruault, Y.
  • An algorithm for solving a nonlinear integro‐differential equation
    Deeba, E.; Khuri, S.A.; Shishen, X.
  • Necessary conditions for the appearance of noise terms in decomposition solution series
    Wazwaz, A.M.
  • A comparison between Adomian decomposition method and Taylor series method in the series solutions
    Wazwaz, A.M.

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