A numerical solution of the sine-Gordon equation using the modified decomposition method

Authors:
Dogan Kaya
Affiliations:
Department of Mathematics, Firat University, Elazig 23119, Turkey
Venue:
Applied Mathematics and Computation
Year:
2003

Citing 4
Cited 3

On the numerical solution of the sine-Gordon equation. I: integrable discretizations and homoclinic manifolds

Journal of Computational Physics
On the numerical solution of the sine-Gordon equation II: performance of numerical schemes

Journal of Computational Physics
A reliable modification of Adomian decomposition method

Applied Mathematics and Computation
Discrete singular convolution for the sine-Gordon equation

Physica D

A new algorithm for the decomposition solution of nonlinear differential equations

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An analytical approach to the sine-Gordon equation using the modified homotopy perturbation method

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An application of the decompositionmethod for the two-dimensional KdV-Burgers equation

Computers & Mathematics with Applications

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Abstract

The decomposition method for solving the sine-Gordon equation has been implemented. By using a number of initial values, the explicit and numerical solutions of the equation are calculated in the form of convergent power series with easily computable components. The present method performs extremely well in terms of accuracy, efficiency, simplicity, stability and reliability.