Integrated High Accuracy Multiquadric Quasi-interpolation Scheme for Solving the Nonlinear Klein-gordon Equation

Volume 14, Issue 4, pp 258-273 http://dx.doi.org/10.22436/jmcs.014.04.01

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Authors

Maryam Sarboland - Department of Mathematics, Saveh Branch, Islamic Azad University, P.O. Box: 39187-366, Saveh, Iran, Azim Aminataei - Faculty of Mathematics, Department of Applied Mathematics, K. N. Toosi University of Technology, P.O. Box: 15418-49611, Tehran, Iran.

Abstract

A collocation scheme based on the use of the multiquadric quasi-interpolation operator \(L_{w_2}\) , integrated radial basis function networks (IRBFNs) method and three order finite difference method is applied to the nonlinear Klein-Gordon equation. In the present scheme, the three order finite difference method is used to discretize the temporal derivative and the integrated form of the multiquadric quasi-interpolation scheme is used to approximate the unknown function and its spatial derivatives. Several numerical experiments are provided to show the efficiency and the accuracy of the given method.

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Keywords

• Nonlinear Klein-Gordon equation
• multiquadric quasi-interpolation scheme
• collocation scheme
• integrated radial basis function networks.

MSC

•  65D10
•  65D05
•  65M70

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