Numerical solution of nonlinear system of Klein–Gordon equations by cubic B-spline collocation method

References

• A.G. Bratsos, On the numerical solution of the Klein–Gordon equation, Numer. Methods Partial Differ. Equ. 25(4) (2009), pp. 939–951. doi: 10.1002/num.20383
   Web of Science ®Google Scholar
• P.J. Caudrey, J.C. Eilbeck, and J.D. Gibbon, The sine-Gordon equation as a model classical field theory, Il Nuovo Cimento B (11) 25(2) (1975), pp. 497–512. doi: 10.1007/BF02724733
   Web of Science ®Google Scholar
• E.Y. Deeba and S.A. Khuri, A decomposition method for solving the nonlinear Klein–Gordon equation, J. Comput. Phys. 124(2) (1996), pp. 442–448. doi: 10.1006/jcph.1996.0071
   Web of Science ®Google Scholar
• M. Dehghan and A. Ghesmati, Application of the dual reciprocity boundary integral equation technique to solve the nonlinear Klein–Gordon equation, Comput. Phys. Comm. 181(8) (2010), pp. 1410–1418. doi: 10.1016/j.cpc.2010.04.008
   Web of Science ®Google Scholar
• M. Dehghan, A. Mohebbi, and Z. Asgari, Fourth-order compact solution of the nonlinear Klein–Gordon equation, Numer. Algorithms 52(4) (2009), pp. 523–540. doi: 10.1007/s11075-009-9296-x
   Web of Science ®Google Scholar
• M. Dehghan and A. Shokri, Numerical solution of the nonlinear Klein–Gordon equation using radial basis functions, J. Comput. Appl. Math. 230(2) (2009), pp. 400–410. doi: 10.1016/j.cam.2008.12.011
   Web of Science ®Google Scholar
• R.K. Dodd, J.C. Eilbeck, J.D. Gibbon, and H.C. Morris, Solitons and Nonlinear Wave Equations. Academic Press, London/New York, 1982.
   Google Scholar
• S. Gottlieb, C. Shu, and E. Tadmor, Strong stability-preserving high-order time discretization methods, SIAM Rev 43(1) (2001), pp. 89–112. doi: 10.1137/S003614450036757X
   Web of Science ®Google Scholar
• J. Hong, S. Jiang, L. Kong, and C. Li, Numerical comparison of five difference schemes for coupled Klein–Gordon–Schrödinger equations in quantum physics, J. Phys. A 40(30) (2007), pp. 9125–9135. doi: 10.1088/1751-8113/40/30/030
   Google Scholar
• L. Kong, R. Liu, and Z. Xu, Numerical simulation of interaction between Schrödinger field and Klein–Gordon field by multisymplectic method, Appl. Math. Comput. 181(1) (2006), pp. 342–350. doi: 10.1016/j.amc.2006.01.044
   Web of Science ®Google Scholar
• L. Kong, J. Hong, and R. Liu, Long-term numerical simulation of the interaction between a neutron field and a neutral meson field by a symplectic-preserving scheme, J. Phys. A 41(25) (2008), p. 255207. doi: 10.1088/1751-8113/41/25/255207
   Google Scholar
• L. Kong, J. Zhang, Y. Cao, Y. Duan, and H. Huang, Semi-explicit symplectic partitioned Runge–Kutta Fourier pseudo-spectral scheme for Klein–Gordon–Schrödinger equations, Comput. Phys. Comm. 181(8) (2010), pp. 1369–1377. doi: 10.1016/j.cpc.2010.04.003
   Web of Science ®Google Scholar
• M. Lakestani and M. Dehghan, Collocation and finite difference-collocation methods for the solution of nonlinear Klein–Gordon equation, Comput. Phys. Comm. 181(8) (2010), pp. 1392–1401. doi: 10.1016/j.cpc.2010.04.006
   Web of Science ®Google Scholar
• I.J. Lee, Numerical solution for nonlinear Klein–Gordon equation by collocation method with respect to spectral method, J. Korean Math. Soc. 32(3) (1995), pp. 541–551.
   Google Scholar
• Q. Li, Z. Ji, Z. Zheng, and H. Liu, Numerical solution of nonlinear Klein–Gordon equation using lattice Boltzmann method, Appl Math. 2(12) (2011), pp. 1479–1485. doi: 10.4236/am.2011.212210
   Google Scholar
• R.C. Mittal and R. Bhatia, Numerical solution of second order one dimensional hyperbolic telegraph equation by cubic B-spline collocation method, Appl. Math. Comput. 220 (2013), pp. 496–506. doi: 10.1016/j.amc.2013.05.081
   Web of Science ®Google Scholar
• R.C. Mittal and R. Bhatia, Numerical solution of nonlinear sine-Gordon equation by modified cubic B-spline collocation method, Int. J. Partial Differ. Equ. 2014 (2014), pp. 1–8. doi: 10.1155/2014/343497
   Google Scholar
• R.C. Mittal and R.K. Jain, Cubic B-splines collocation method for solving nonlinear parabolic partial differential equations with Neumann boundary conditions, Commun. Nonlinear Sci. Numer. Simul. 17(12) (2012), pp. 4616–4625. doi: 10.1016/j.cnsns.2012.05.007
   Web of Science ®Google Scholar
• R.C. Mittal and R.K. Jain, Numerical solutions of nonlinear Fisher's reaction-diffusion equation with modified cubic B-spline collocation method, Math. Sci. (Springer) 7(12) (2013), p. 10.
   Google Scholar
• J. Rashidinia and R. Mohammadi, Tension spline approach for the numerical solution of nonlinear Klein–Gordon equation, Comput. Phys. Comm. 181(1) (2010), pp. 78–91. doi: 10.1016/j.cpc.2009.09.001
   Web of Science ®Google Scholar
• J. Rashidinia, M. Ghasemi, and R. Jalilian, Numerical solution of the nonlinear Klein–Gordon equation, J. Comput. Appl. Math. 233(8) (2010), pp. 1866–1878. doi: 10.1016/j.cam.2009.09.023
   Web of Science ®Google Scholar
• J. Rashidinia, F. Esfahani, and S. Jamalzadeh, B-spline collocation approach for solution of Klein–Gordon equation, Int. J. Math. Model. Comput. 3(1) (2013), pp. 25–33.
   Google Scholar
• A.S.V. Ravi Kanth, and K. Aruna, Differential transform method for solving the linear and nonlinear Klein–Gordon equation, Comput. Phys. Commun. 180(5) (2009), pp. 708–711. doi: 10.1016/j.cpc.2008.11.012
   Web of Science ®Google Scholar
• M. Wang and Y. Zhou, The periodic wave solutions for the Klein–Gordon–Schrödinger equations, Phys. Lett. A 318(1/2) (2003), pp. 84–92. doi: 10.1016/j.physleta.2003.07.026
   Web of Science ®Google Scholar