Numerical solution of the nonlinear Klein-Gordon equation

Journal of Computational and Applied Mathematics

Volumn 233, Issue 8, 2010, Pages 1866-1878

  Rashidinia, J ^a   Ghasemi, M ^a   Jalilian, R ^b  

^a IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

^b ILAM UNIVERSITY   (Iran)

Author keywords

Collocation; Convergence analysis; Cubic B spline method; Nonlinear Klein Gordon equation

Indexed keywords

CONVERGENCE ANALYSIS; CONVERGENCE AND STABILITY; CUBIC B -SPLINE; DIRICHLET AND NEUMANN BOUNDARY CONDITIONS; EXACT SOLUTION; KLEIN-GORDON EQUATION; NONLINEAR KLEIN-GORDON EQUATION; NUMERICAL RESULTS; NUMERICAL SOLUTION; ROOT-MEAN-SQUARE ERRORS; TEST EXAMPLES; UNIFORM MESH;

LINEAR EQUATIONS; SPLINES;

NONLINEAR EQUATIONS;

EID: 70549087999     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.09.023     Document Type: Article

References (24)

1. Han H., and Zhang Z. Split local absorbing conditions for one-dimensional nonlinear Klein-Gordon equation on unbounded domain. Journal of Computational Physics 227 (2008) 8992-9004
2. Wazwaz A. New traveling wave solutions to the boussinesq and the Klein-Gordon equations. Communications in Nonlinear Science and Numerical Simulation 13 (2008) 889-901
3. Fabian A.L., Kohl R., and Biswas A. Perturbation of topological solitons due to sine-gordon equation and its type. Communications in Nonlinear Science and Numerical Simulation 14 4 (2009) 1227-1244
4. Dehghan M., and Shokri A. Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions. Journal of Computational and Applied Mathematics 230 (2009) 400-410
5. Dehghan M., and Shokri A. A numerical method for solution of the two-dimensional sine-gordon equation using the radial basis functions. Mathematics and Computers in Simulation 79 (2008) 700-715
6. Sirendaoreji. Auxiliary equation method and new solutions of Klein. Chaos, Solitons and Fractals 31 (2007) 943-950
7. Sirendaoreji. A new auxiliary equation and exact traveling wave solutions of nonlinear equations. Physics Letters A 356 (2006) 124-130
8. Shakeri F., and Dehghan M. Numerical solution of the Klein-Gordon equation via he's variational iteration method. Nonlinear Dynamics 51 (2008) 89-97
9. S.M.El-Sayed. The decomposition method for studying the Klein-Gordon equation. Chaos, Solitons and Fractals 18 (2003) 1025-1030
10. Lynch M. Large amplitude instability in finite difference approximations to the Klein-Gordon equation. Applied Numerical Mathematics 31 (1999) 173-182
11. Strauss W., and Vazquez L. Numerical solution of a nonlinear Klein-Gordon equation. Journal of Computational Physics 28 (1978) 271-278
12. Kaya D., and El-Sayed S. A numerical solution of the Klein-Gordon equation and convergence of the decomposition method. Applied Mathematics and Computation 156 (2004) 341-353
13. Li X., and Guo B. A legendre spectral method for solving nonlinear Klein-Gordon equation. Journal of Computational Mathematics 15 (1997) 105-126
14. Jiminez S., and Vazquez L. Analysis of four numerical schemes for a nonlinear Klein-Gordon equation. Applied Mathematics Computation 35 (1990) 61-94
15. Kadalbajoo M.K., Gupta V., and Awasthi A. A uniformly convergent b-spline collocation method on a nonuniform mesh for singularly perturbed one-dimensional time-dependent linear convection diffusion problem. Journal of Computational and Applied Mathematics 220 (2008) 271-289
16. Dag I., Sakab B., and Irkb D. Galerkin method for the numerical solution of the rlw equation using quintic b-splines. Journal of Computational and Applied Mathematics 190 (2006) 532-547
17. Khalifaa A., Raslana K., and Alzubaidib H. A collocation method with cubic b-splines for solving the mrlw equation. Journal of Computational and Applied Mathematics 212 (2008) 406-418
18. Kutluay S., Bahadir A., and Ozdes A. Numerical solution of one-dimensional burgers' equation: Explicit and exact-explicit finite difference methods. Journal of Computational and Applied Mathematics 103 (1999) 251-261
19. Kutluay S., Esen A., and Dag I. Numerical solutions of the burgers' equation by the least squares quadratic b-spline finite element method. Journal of Computational and Applied Mathematics 167 (2004) 21-31
20. Mohanty R., Jain M., and George K. Fourth-order approximations at first time level, linear stability analysis and the numerical solution of multidimensional second-order nonlinear hyperbolic equations in polar coordinates. Journal of Computational and Applied Mathematics 93 (1998) 1-12
21. Prenter P.M. Spline and Variational Methods (1975), Wiley, New York
22. de Boor C. On the convergence of odd degree spline interpolation. Journal of Approximation Theory 1 (1968) 452-463
23. Hall C.A. On error bounds for spline interpolation. Journal of Approximation Theory 1 (1968) 209-218
24. Rudin W. Principles of Mathematical Analysis. third ed. (1976), McGraw-Hill Inc.