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Year 2017, Volume: 5 Issue: 1, 114 - 127, 01.01.2017

Abstract

References

  • S. M. Hoseini and T. R. Marchant, Solitary wave interaction and evolution for Higher order Hirota equation, Wave Motion. Vol. 44, pp. 92-106, 2006.
  • W. G. Al.Harbi, Numerical Solution of Hirota Equation, M.S.C., KAU, 2009.
  • I. Christie, D. Griffiths, A. Mitchell, and J. M. Sanz-Serna, Product Approximation for non-linear problems in the finite element method, IMA J. N. A. Vol. 1, pp. 253- 266, 1981.
  • J. M. Sanz-Serna and I. Christsie, Petrov- Galerkin methods for nonlinear dispersive waves, J. Comp. Phys. Vol. 39, pp. 94-103, 1981.
  • R.T. Taha and M. J. Ablowitz, Analytical and numerical aspects of certain Nonlinear evolution equations. IV. Numerical, Korteweg-de Vries equation, J. Comput. Phys. Vol. 55, pp. 231-253, 1984.
  • R. T. Taha and M. J. Ablowitz, Analytical and numerical aspects of certain Nonlinear evolution equation. IV. Numerical, Modi.ed Korteweg-de Vries equation, J. Comput. Phys. Vol. 77, pp. 540-548, 1988.
  • S. S. Al.Sairy, A Linearly Implicit schemes for the coupled nonlinear Schrödinger Equation, M. S.C., KAU, 2006.
  • R. T. Taha and M. J. Ablowitz, Analytical and numerical aspects of certain Nonlinear evolution equation. II. Numerical, nonlinear Schrödinger equation, J. Comput. Phys. Vol. 55, pp. 203-230, 1984.
  • M.S. Ismail and R.T. Taha, Numerical Simulation of Coupled Nonlinear Schrödinger equation, Math. Comp. Simul. Vol. 56, pp. 547-562, 2001.
  • M. S. Ismail and S. Z. Alamri, Highly Accurate Finite Difference Method for Coupled Nonlinear Schrödinger equation, Int. J. Comp. Math. Vol. 81(3), pp. 303-351, 2004.
  • M. S. Ismail and R. T. Taha, A Linearly Implicit Conservative Scheme for the Coupled Nonlinerar Schrödinger equation, Math. Comp. Simul. Vol. 74, pp. 302-311, 2007.
  • M. S. Ismail, Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method, Math. Comp. Simul. Vol. 78, pp. 532-547, 2008.
  • A. A. Halim S. B. Kshevetskii and S. B. Leble, Numerical integration of a Coupled Korteweg-de Vries System, Comput. And Math Applic. Vol.45, pp.581-591, 2003.
  • A. A. Halim and S. B. Leble, Analytical and numerical solution of coupled KdV-MKdV system, Chaos, Solitons, Fractals. Vol. 19, pp. 99-108, 2004
  • M. S. Ismail, Numerical solution of Coupled Korteweg-de Vries equation by Collocation method, NMPDE. Vol. 25, pp. 275-291, 2009.
  • S. Zhu, A difference scheme for the coupled KdV Equation, Communication in Nonlinear Science and Numerical Simulation Vol. 4 (1), pp. 69-63, 1999.
  • M. S. Ismail, Numerical solution of Complex Modified Korteweg-de Vries equation by collocation method, CNSNS. Vol. 14, pp. 749-759, 2009.
  • M. S. Ismail, Numerical solution of Complex Modified Korteweg-de Vries equation by Petrov-Galerkin method, App. math and comput. Vol. 202, pp. 520- 531, 2008.
  • G. M. Muslu and H. A.Erlbay, A split-Step Fourier Method for the Complex Modified Korteweg-de Vries Equation, Comput. Math Applic.Vol.45, pp. 503-514, 2003.
  • R. T. Taha, Numerical Simulations of complex Modified Korteweg-de Vries equation, Math. comput. Simul. Vol. 37, pp. 461-467, 1994.
  • A. M. Wazwaz, The Tanh and the Sine-Cosine Methods for the Complex Modified KdV Equation and the Generalized KdV Equation, Comput. Math. Applic. Vol. 49, pp. 1101-1112, 2005.
  • T. S. EL-Danaf, K. R. Raslan and Khalid K. Ali,"New Numerical treatment for the Generalized Regularized Long Wave Equation based on finite difference scheme", Int. J. of S. Comp. and Eng. (IJSCE)’, Vol. 4, pp. 16-24, 2014.
  • T. S. EL-Danaf, K. R. Raslan and Khalid K. Ali," collocation method with cubic B-Splines for solving the GRLW equation", Int. J. of Num. Meth. and Appl. Vol. 15 (1), pp. 39-59, 2016.

Finite difference method with different high order approximations for solving complex equation

Year 2017, Volume: 5 Issue: 1, 114 - 127, 01.01.2017

Abstract


References

  • S. M. Hoseini and T. R. Marchant, Solitary wave interaction and evolution for Higher order Hirota equation, Wave Motion. Vol. 44, pp. 92-106, 2006.
  • W. G. Al.Harbi, Numerical Solution of Hirota Equation, M.S.C., KAU, 2009.
  • I. Christie, D. Griffiths, A. Mitchell, and J. M. Sanz-Serna, Product Approximation for non-linear problems in the finite element method, IMA J. N. A. Vol. 1, pp. 253- 266, 1981.
  • J. M. Sanz-Serna and I. Christsie, Petrov- Galerkin methods for nonlinear dispersive waves, J. Comp. Phys. Vol. 39, pp. 94-103, 1981.
  • R.T. Taha and M. J. Ablowitz, Analytical and numerical aspects of certain Nonlinear evolution equations. IV. Numerical, Korteweg-de Vries equation, J. Comput. Phys. Vol. 55, pp. 231-253, 1984.
  • R. T. Taha and M. J. Ablowitz, Analytical and numerical aspects of certain Nonlinear evolution equation. IV. Numerical, Modi.ed Korteweg-de Vries equation, J. Comput. Phys. Vol. 77, pp. 540-548, 1988.
  • S. S. Al.Sairy, A Linearly Implicit schemes for the coupled nonlinear Schrödinger Equation, M. S.C., KAU, 2006.
  • R. T. Taha and M. J. Ablowitz, Analytical and numerical aspects of certain Nonlinear evolution equation. II. Numerical, nonlinear Schrödinger equation, J. Comput. Phys. Vol. 55, pp. 203-230, 1984.
  • M.S. Ismail and R.T. Taha, Numerical Simulation of Coupled Nonlinear Schrödinger equation, Math. Comp. Simul. Vol. 56, pp. 547-562, 2001.
  • M. S. Ismail and S. Z. Alamri, Highly Accurate Finite Difference Method for Coupled Nonlinear Schrödinger equation, Int. J. Comp. Math. Vol. 81(3), pp. 303-351, 2004.
  • M. S. Ismail and R. T. Taha, A Linearly Implicit Conservative Scheme for the Coupled Nonlinerar Schrödinger equation, Math. Comp. Simul. Vol. 74, pp. 302-311, 2007.
  • M. S. Ismail, Numerical solution of coupled nonlinear Schrödinger equation by Galerkin method, Math. Comp. Simul. Vol. 78, pp. 532-547, 2008.
  • A. A. Halim S. B. Kshevetskii and S. B. Leble, Numerical integration of a Coupled Korteweg-de Vries System, Comput. And Math Applic. Vol.45, pp.581-591, 2003.
  • A. A. Halim and S. B. Leble, Analytical and numerical solution of coupled KdV-MKdV system, Chaos, Solitons, Fractals. Vol. 19, pp. 99-108, 2004
  • M. S. Ismail, Numerical solution of Coupled Korteweg-de Vries equation by Collocation method, NMPDE. Vol. 25, pp. 275-291, 2009.
  • S. Zhu, A difference scheme for the coupled KdV Equation, Communication in Nonlinear Science and Numerical Simulation Vol. 4 (1), pp. 69-63, 1999.
  • M. S. Ismail, Numerical solution of Complex Modified Korteweg-de Vries equation by collocation method, CNSNS. Vol. 14, pp. 749-759, 2009.
  • M. S. Ismail, Numerical solution of Complex Modified Korteweg-de Vries equation by Petrov-Galerkin method, App. math and comput. Vol. 202, pp. 520- 531, 2008.
  • G. M. Muslu and H. A.Erlbay, A split-Step Fourier Method for the Complex Modified Korteweg-de Vries Equation, Comput. Math Applic.Vol.45, pp. 503-514, 2003.
  • R. T. Taha, Numerical Simulations of complex Modified Korteweg-de Vries equation, Math. comput. Simul. Vol. 37, pp. 461-467, 1994.
  • A. M. Wazwaz, The Tanh and the Sine-Cosine Methods for the Complex Modified KdV Equation and the Generalized KdV Equation, Comput. Math. Applic. Vol. 49, pp. 1101-1112, 2005.
  • T. S. EL-Danaf, K. R. Raslan and Khalid K. Ali,"New Numerical treatment for the Generalized Regularized Long Wave Equation based on finite difference scheme", Int. J. of S. Comp. and Eng. (IJSCE)’, Vol. 4, pp. 16-24, 2014.
  • T. S. EL-Danaf, K. R. Raslan and Khalid K. Ali," collocation method with cubic B-Splines for solving the GRLW equation", Int. J. of Num. Meth. and Appl. Vol. 15 (1), pp. 39-59, 2016.
There are 23 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Kamal Raslan Raslan This is me

Talaat S. El-danaf This is me

Khalid K. Ali This is me

Publication Date January 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Raslan, K. R., El-danaf, T. S., & Ali, K. K. (2017). Finite difference method with different high order approximations for solving complex equation. New Trends in Mathematical Sciences, 5(1), 114-127.
AMA Raslan KR, El-danaf TS, Ali KK. Finite difference method with different high order approximations for solving complex equation. New Trends in Mathematical Sciences. January 2017;5(1):114-127.
Chicago Raslan, Kamal Raslan, Talaat S. El-danaf, and Khalid K. Ali. “Finite Difference Method With Different High Order Approximations for Solving Complex Equation”. New Trends in Mathematical Sciences 5, no. 1 (January 2017): 114-27.
EndNote Raslan KR, El-danaf TS, Ali KK (January 1, 2017) Finite difference method with different high order approximations for solving complex equation. New Trends in Mathematical Sciences 5 1 114–127.
IEEE K. R. Raslan, T. S. El-danaf, and K. K. Ali, “Finite difference method with different high order approximations for solving complex equation”, New Trends in Mathematical Sciences, vol. 5, no. 1, pp. 114–127, 2017.
ISNAD Raslan, Kamal Raslan et al. “Finite Difference Method With Different High Order Approximations for Solving Complex Equation”. New Trends in Mathematical Sciences 5/1 (January 2017), 114-127.
JAMA Raslan KR, El-danaf TS, Ali KK. Finite difference method with different high order approximations for solving complex equation. New Trends in Mathematical Sciences. 2017;5:114–127.
MLA Raslan, Kamal Raslan et al. “Finite Difference Method With Different High Order Approximations for Solving Complex Equation”. New Trends in Mathematical Sciences, vol. 5, no. 1, 2017, pp. 114-27.
Vancouver Raslan KR, El-danaf TS, Ali KK. Finite difference method with different high order approximations for solving complex equation. New Trends in Mathematical Sciences. 2017;5(1):114-27.