Fourth‐order compact and energy conservative scheme for solving nonlinear Klein‐Gordon equation

[1]  Salvador Jiménez,et al.  Derivation of the discrete conservation laws for a family of finite difference schemes , 1994 .

[2]  Mehdi Dehghan,et al.  Fourth-order compact solution of the nonlinear Klein-Gordon equation , 2009, Numerical Algorithms.

[3]  N. Zabusky,et al.  Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States , 1965 .

[4]  Mark J. Ablowitz,et al.  Regular ArticleOn the Numerical Solution of the Sine–Gordon Equation: I. Integrable Discretizations and Homoclinic Manifolds , 1996 .

[5]  A. G. Bratsos A numerical method for the one‐dimensional sine‐Gordon equation , 2008 .

[6]  Z. Fei,et al.  Two energy conserving numerical schemes for the Sine-Gordon equation , 1991 .

[7]  A. G. Bratsos On the numerical solution of the Klein-Gordon equation , 2009 .

[8]  Changying Liu,et al.  An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations , 2014, Appl. Math. Comput..

[9]  Mehdi Dehghan,et al.  Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices , 2006, Math. Comput. Simul..

[10]  W. Strauss,et al.  Numerical solution of a nonlinear Klein-Gordon equation , 1978 .

[11]  Tingchun Wang,et al.  Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions , 2013, J. Comput. Phys..

[12]  William E. Schiesser,et al.  A Compendium of Partial Differential Equation Models: Frontmatter , 2009 .

[13]  L. Vázquez,et al.  Numerical solution of the sine-Gordon equation , 1986 .

[14]  Mark J. Ablowitz,et al.  Numerical simulation of quasi-periodic solutions of the sine-Gordon equation , 1995 .

[15]  Mehdi Dehghan,et al.  High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods , 2010, Math. Comput. Model..

[16]  Mark J. Ablowitz,et al.  On the Numerical Solution of the Sine-Gordon Equation , 1996 .

[17]  Jianlin Xia,et al.  Order conditions for ARKN methods solving oscillatory systems , 2009, Comput. Phys. Commun..

[18]  Abdul-Majid Wazwaz,et al.  Compactons, solitons and periodic solutions for some forms of nonlinear Klein–Gordon equations , 2006 .

[19]  Mehdi Dehghan,et al.  On the solution of an initial‐boundary value problem that combines Neumann and integral condition for the wave equation , 2005 .