An efficient spectral collocation algorithm for nonlinear Phi-four equations

Springer Science and Business Media LLC - Tập 2013 Số 1 - 2013
A. H. Bhrawy1, Laila M Assas1, Mohammed Alghamdi1
1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

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Canuto C, Hussaini MY, Quarteroni A, Zang TA: Spectral Methods: Fundamentals in Single Domains. Springer, New York; 2006.

Doha EH, Bhrawy AH: An efficient direct solver for multidimensional elliptic robin boundary value problems using a Legendre spectral-Galerkin method. Comput. Math. Appl. 2012, 64: 558-571. 10.1016/j.camwa.2011.12.050

Kamrani M, Hosseini SM: Spectral collocation method for stochastic Burgers equation driven by additive noise. Math. Comput. Simul. 2012, 82: 1630-1644. 10.1016/j.matcom.2012.03.007

Saadatmandi A, Dehghan M: A tau approach for solution of the space fractional diffusion equation. Comput. Math. Appl. 2011, 62: 1135-1142. 10.1016/j.camwa.2011.04.014

Bhrawy AH, Alshomrani M: A shifted Legendre spectral method for fractional-order multi-point boundary value problems. Adv. Differ. Equ. 2012., 2012: Article ID 8

Bhrawy AH, Alofi AS: The operational matrix of fractional integration for shifted Chebyshev polynomials. Appl. Math. Lett. 2013, 26: 25-31. 10.1016/j.aml.2012.01.027

Guo BY, Yan JP: Legendre-Gauss collocation method for initial value problems of second order ordinary differential equations. Appl. Numer. Math. 2009, 59: 1386-1408. 10.1016/j.apnum.2008.08.007

Doha EH, Bhrawy AH, Ezz-Eldien SS: A new Jacobi operational matrix: an application for solving fractional differential equation. Appl. Math. Model. 2012, 36: 4931-4943. 10.1016/j.apm.2011.12.031

Saadatmandi A, Dehghan M: The use of Sinc-collocation method for solving multi-point boundary value problems. Commun. Nonlinear Sci. Numer. Simul. 2012, 17: 593-601. 10.1016/j.cnsns.2011.06.018

Bhrawy AH, Alofi AS: A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations. Commun. Nonlinear Sci. Numer. Simul. 2012, 17: 62-70. 10.1016/j.cnsns.2011.04.025

Doha EH, Bhrawy AH, Hafez RM: On shifted Jacobi spectral method for high-order multi-point boundary value problems. Commun. Nonlinear Sci. Numer. Simul. 2012, 17: 3802-3810. 10.1016/j.cnsns.2012.02.027

Wang ML, Zhou YB: The periodic wave solutions for the Klein-Gordon-Schrodinger equations. Phys. Lett. A 2003, 318: 84-92. 10.1016/j.physleta.2003.07.026

Yomba E: On exact solutions of the coupled Klein-Gordon-Schrodinger and the complex coupled KdV equations using mapping method. Chaos Solitons Fractals 2004, 21: 209. 10.1016/j.chaos.2003.10.028

Li XY, Yang S, Wang ML:The periodic wave solutions for the ( 3 + 1 ) -dimensional Klein-Gordon-Schrodinger equations. Chaos Solitons Fractals 2005, 25: 629-636. 10.1016/j.chaos.2004.11.028

Arafa AAM, Rida SZ: Numerical solutions for some generalized coupled nonlinear evolution equations. Math. Comput. Model. 2012, 56: 268-277. 10.1016/j.mcm.2011.12.046

Jiwari R, Mittal RC, Sharma KK: A numerical scheme based on weighted average differential quadrature method for the numerical solution of Burgers’ equation. Appl. Math. Comput. 2013, 219: 6680-6691. 10.1016/j.amc.2012.12.035

Bhrawy AH, Al-shomrani M: A Jacobi Dual-Petrov Galerkin-Jacobi Collocation Method for Solving Korteweg-de Vries equations. Abstr. Appl. Anal. 2012., 2012: Article ID 16

Khan Y: A method for solving nonlinear time-dependent drainage model. Neural Comput. Appl. 2013. doi:10.1007/s00521-012-0933-2

Khan Y, Diblik J, Faraz N, Smarda Z: An efficient new perturbative Laplace method for space-time fractional telegraph equations. Adv. Differ. Equ. 2012., 2012: Article ID 204

El-Kady M, El-Sayed SM, Fathy HE: Development of Galerkin method for solving the generalized Burger’s-Huxley equation. Math. Probl. Eng. 2013., 2013: Article ID 9

Van Gorder RA, Vajravelu K: Analytical and numerical solutions of the density dependent Nagumo telegraph equation. Nonlinear Anal., Real World Appl. 2010, 11: 3923-3929. 10.1016/j.nonrwa.2010.02.019

Dehghan M, Mohebbi A, Asgari Z: Fourth-order compact solution of the nonlinear Klein-Gordon equation. Numer. Algorithms 2009, 52: 523-540. 10.1007/s11075-009-9296-x

Chowdhury A, Biswas A: Singular solitons and numerical analysis of phi-four equation. Math. Sci. 2012., 6: Article ID 42

Sassaman R, Biswas A: Soliton perturbation theory for Phi-four model and nonlinear Klein-Gordon equations. Commun. Nonlinear Sci. Numer. Simul. 2009, 14: 3239-3249. 10.1016/j.cnsns.2008.12.020

Khater AH, Callebaut DK, Bhrawy AH, Abdelkawy MA: Nonlinear periodic solutions for isothermal magnetostatic atmospheres. J. Comput. Appl. Math. 2013, 242: 28-40.

Soliman AA: Exact traveling wave solution of nonlinear variants of the RLW and the PHI-four equations. Phys. Lett. A 2007, 368: 383-390. 10.1016/j.physleta.2007.04.040

Triki H, Wazwaz A: Envelope solitons for generalized forms of the phi-four equation. Journal of King Saud University. Science 2012. doi:10.1016/j.jksus.2012.08.001

Zhou H, Shen J: Bifurcations of travelling wave solutions for modified nonlinear dispersive phi-four equation. Appl. Math. Comput. 2010, 217: 1584-1597. 10.1016/j.amc.2009.07.001

Deng X, Zhao M, Li X: Travelling wave solutions for a nonlinear variant of the Phi-four equation. Math. Comput. Model. 2009, 49: 617-622. 10.1016/j.mcm.2008.03.011

Russo M, Van Gorder RA, Choudhury SR: Painleve property and exact solutions for a nonlinear wave equation with generalized power-law nonlinearities. Commun. Nonlinear Sci. Numer. Simul. 2013, 18: 1623-1634. 10.1016/j.cnsns.2012.11.019

Van Gorder RA, Sweet E, Vajravelu K: Analytical solutions of a coupled nonlinear system arising in a flow between stretching disks. Appl. Math. Comput. 2010, 216: 1513-1523. 10.1016/j.amc.2010.02.053

Doha EH, Bhrawy AH: A Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations. Numer. Methods Partial Differ. Equ. 2009, 25: 712-739. 10.1002/num.20369

Bhrawy AH, Alghamdi MA: A shifted Jacobi-Gauss-Lobatto collocation method for solving nonlinear factional Langevin equation involving two fractional orders in different intervals. Bound. Value Probl. 2012., 2012: Article ID 62

Fan E, Hon YC: Generalized tanh method extended to special types of nonlinear equations. Z. Naturforsch. 2002, 57a: 692-700.