Numerical solution of the nonlinear Klein-Gordon equation

Authors:
J. Rashidinia;M. Ghasemi;R. Jalilian
Affiliations:
School of Mathematics, Iran University of Science & Technology, Narmak, Tehran 16844, Iran;School of Mathematics, Iran University of Science & Technology, Narmak, Tehran 16844, Iran;Department of Mathematics, Ilam University, PO Box 69315-516, Ilam, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

A numerical method is developed to solve the nonlinear one-dimensional Klein-Gordon equation by using the cubic B-spline collocation method on the uniform mesh points. We solve the problem for both Dirichlet and Neumann boundary conditions. The convergence and stability of the method are proved. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L"2, L"~ and Root-Mean-Square errors (RMS) in the solutions show the efficiency of the method computationally.