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Research Article Open access CC BY 4.0

Numerical Solutions of Coupled Nonlinear Evolution Equations via El-gendi Nodal Galerkin Method

M. El-Kady, Salah M. El-Sayed, Heba. E. Salem

Journal of Advances in Mathematics and Computer Science · pp. 310–332 · Published 4 Nov 2014

10.9734/BJMCS/2015/8245

Abstract

In this research the solution of coupled modified Korteweg-de Vries equation (mKdV) and the generalized Hirota–Satsuma coupled KdV equation by using El-gendi nodal Galerkin (EGG) approaches are presented. El-gendi nodal Galerkin (EGG) (EGG) approaches consist of two approaches, the first is El-gendi Chebyshev nodal Galerkin (ECG) and the second approach is called El-gendi Legendre nodal Galerkin (ELG). In these new approaches spaces of the solution and the weak form to the system are presented. The resulted systems of ODES are solved by the fourth order Runge-Kutta solver. The convergence and the stability of these new methods are analyzed numerically. Numerical results are presented and compared with the results obtained by pseudo-spectral method.

Coupled mKdV equation generalized Hirota-Satsuma Coupled KdV equation El-gendi nodal Galerkin method Legendre and Chebyshev cardinal functions

References (15)

  1. 1 Spectral Methods in MATLAB [DOI]
  2. 2 Spectral Methods: Fundamentals in Single Domains [DOI]
  3. 3 Spectral methods for hyperbolic problems [DOI]
  4. 4 Soliton solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled MKdV equation [DOI]
  5. 5 Chebyshev Solution of Differential, Integral and Integro-Differential Equations [DOI]
  6. 6 A generalized Hirota–Satsuma coupled Korteweg–de Vries equation and Miura transformations [DOI]
  7. 7 An Instability Phenomenon in Spectral Methods [DOI]
  8. 8 Higher order pseudospectral differentiation matrices [DOI]
  9. 9 Efficient spectral-Galerkin methods for systems of coupled second-order equations and their applications [DOI]
  10. 10 Numerical solutions for some coupled nonlinear evolution equations by using spectral collocation method [DOI]
  11. 11 The decomposition method for a Hirota–Satsuma coupled KdV equation and a coupled MKdV equation [DOI]
  12. 12 On Using the Homotopy Perturbation Method for Finding the Travelling Wave Solutions of Generalized Nonlinear Hirota- Satsuma Coupled KdV Equations
  13. 13 INTERACTIVE CHEBYSHEV–LEGENDRE ALGORITHM FOR LINEAR QUADRATIC OPTIMAL REGULATOR SYSTEMS [DOI]
  14. 14 Approximate analytic solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled mKdV equation [DOI]
  15. 15 Numerical Solution of Hirota-Satsuma Couple Kdv and a Coupled MKdv Equation by Means of Homotopy Analysis Method

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