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Original Articles

A fourth order numerical scheme for the one-dimensional sine-Gordon equation

Pages 1083-1095 | Received 16 Mar 2007, Accepted 22 May 2007, Published online: 04 Mar 2011

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Read on this site (3)

J. E. Macías-Díaz & A. Puri. (2011) On some explicit non-standard methods to approximate nonnegative solutions of a weakly hyperbolic equation with logistic nonlinearity. International Journal of Computer Mathematics 88:15, pages 3308-3323.
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J. Ruiz-Ramírez & J. E. Macías-Díaz. (2011) A finite-difference scheme to approximate non-negative and bounded solutions of a FitzHugh–Nagumo equation. International Journal of Computer Mathematics 88:15, pages 3186-3201.
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A. G. Bratsos & L. A. Petrakis. (2010) A modified predictor-corrector scheme for the Klein–Gordon equation. International Journal of Computer Mathematics 87:8, pages 1892-1904.
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Articles from other publishers (20)

Suruchi Singh, Swarn Singh & Anu Aggarwal. (2022) Cubic B-spline method for non-linear sine-Gordon equation. Computational and Applied Mathematics 41:8.
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A.H. Msmali, Mohammad Tamsir & Abdullah Ali H. Ahmadini. (2021) Crank-Nicolson-DQM based on cubic exponential B-splines for the approximation of nonlinear Sine-Gordon equation. Ain Shams Engineering Journal 12:4, pages 4091-4097.
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Brajesh Kumar Singh & Mukesh Gupta. (2021) A New Efficient Fourth Order Collocation Scheme for Solving sine–Gordon Equation. International Journal of Applied and Computational Mathematics 7:4.
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Mahmoud Lotfi & Amjad Alipanah. (2019) Legendre spectral element method for solving sine-Gordon equation. Advances in Difference Equations 2019:1.
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Zhengjie Sun. (2019) Multi-symplectic quasi-interpolation method for Hamiltonian partial differential equations. Journal of Computational Physics 395, pages 125-143.
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Francisca Martin-Vergara, Francisco Rus & Francisco R. Villatoro. (2019) Padé numerical schemes for the sine-Gordon equation. Applied Mathematics and Computation 358, pages 232-243.
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A. K. Mittal & L. K. Balyan. Time-space pseudospectral algorithm for numerical solution of Sine/Klein-Gordon equations. Time-space pseudospectral algorithm for numerical solution of Sine/Klein-Gordon equations.
H.S. Shukla & Mohammad Tamsir. (2018) Numerical solution of nonlinear sine–Gordon equation by using the modified cubic B-spline differential quadrature method. Beni-Suef University Journal of Basic and Applied Sciences 7:4, pages 359-366.
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Zhengjie Sun & Zongmin Wu. (2018) Meshless Conservative Scheme for Multivariate Nonlinear Hamiltonian PDEs. Journal of Scientific Computing 76:2, pages 1168-1187.
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Hamid Moghaderi & Mehdi Dehghan. (2014) A multigrid compact finite difference method for solving the one‐dimensional nonlinear sine‐Gordon equation. Mathematical Methods in the Applied Sciences 38:17, pages 3901-3922.
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Ram Jiwari. (2015) Lagrange interpolation and modified cubic B-spline differential quadrature methods for solving hyperbolic partial differential equations with Dirichlet and Neumann boundary conditions. Computer Physics Communications 193, pages 55-65.
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Mohammad Ilati & Mehdi Dehghan. (2015) The use of radial basis functions (RBFs) collocation and RBF-QR methods for solving the coupled nonlinear sine-Gordon equations. Engineering Analysis with Boundary Elements 52, pages 99-109.
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盎然 刘. (2015) A Fourth-Order Compact Finite Volume Scheme for 1D Sine-Gordon Equations. Advances in Applied Mathematics 04:03, pages 262-270.
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Xiaoquan Ding, Qing-Jiang Meng & Li-Ping Yin. (2015) Discrete-Time Orthogonal Spline Collocation Method for One-Dimensional Sine-Gordon Equation. Discrete Dynamics in Nature and Society 2015, pages 1-8.
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R. C. Mittal & Rachna Bhatia. (2014) Numerical Solution of Nonlinear Sine-Gordon Equation by Modified Cubic B-Spline Collocation Method. International Journal of Partial Differential Equations 2014, pages 1-8.
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Ameneh Taleei & Mehdi Dehghan. (2013) A pseudo‐spectral method that uses an overlapping multidomain technique for the numerical solution of sine‐Gordon equation in one and two spatial dimensions. Mathematical Methods in the Applied Sciences 37:13, pages 1909-1923.
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Murat Sari & G?rhan G?rarslan. (2011) A sixth-order compact finite difference method for the one-dimensional sine-Gordon equation. International Journal for Numerical Methods in Biomedical Engineering 27:7, pages 1126-1138.
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A Golbabai & M M Arabshahi. (2011) On the behavior of high-order compact approximations in the one-dimensional sine–Gordon equation. Physica Scripta 83:1, pages 015015.
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Jalil Rashidinia & Reza Mohammadi. (2010) Tension spline solution of nonlinear sine-Gordon equation. Numerical Algorithms 56:1, pages 129-142.
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Akbar Mohebbi & Mehdi Dehghan. (2010) High-order solution of one-dimensional sine–Gordon equation using compact finite difference and DIRKN methods. Mathematical and Computer Modelling 51:5-6, pages 537-549.
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