A NUMERICAL METHOD TO SOLVE THE VISCOSITY PROBLEM OF THE BURGERS EQUATION
Keywords:
Burgers equation, Cole-Hopf transformation, SBA methodDOI:
https://doi.org/10.17654/0974324324008Abstract
Considering the viscosity problem of the Burgers equation, we give a numerical solution using the Cole-Hopf transformation.
Received: January 12, 2024
Accepted: February 27, 2024
References
B. Abbo, Nouvel algorithm numérique de résolution des équations différentielles ordinaries (EDO) et des équations aux dérivées partielles (EDP) non linéaires, Thèse de Doctorat unique, Université de Ouagadougou, 2007.
B. Abbo, B. Some, O. So and G. Barro, A new numerical algorithm for solving nonlinear partial differential equations with initial and boundary conditions, Far East J. Appl. Math. 28(1) (2007), 37-52.
M. Ablowitch and H. Segur, Solitons and the Inverse Scattering Transform, SIAM, 1981.
G. Adomian, A review the decomposition method in applied mathematics, J. Math. Anal. Appl. 135 (1988), 501-544.
G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Pub., 1994.
R. K. Dodd et al., Solution and Nonlinear Wave Equations, Academic Press, New York, 1982.
J.-D. Fournier and U. Frisch, L’équation de burgers déterministe et statistique, Journal de Mécanique Théorique et Appliquée 2(5) (1983), 699-750.
A. Guesima and N. Daili, Approche numérique de la solution entropique de l’équation d’évolution de bürgers par la méthode des lignes, Gen. Math. 17(2) (2009), 99-111.
Ji-Huan He, A new approach to nonlinear partial differential equations, Commun. Nonlinear Sci. Numer. Simul. 2(4) (1997), 230-235.
Ji-Huan He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Meth. Appl. Mech. Eng. 167 (1998), 57-68.
Ji-Huan He, Variational iteration method a kind of nonlinear analytical technique: some examples, Int. J. Non-Linear Mech. 34(4) (1999), 699-708.
Mariana Malard, Sine-Gordon model: renormalization group solution and applications, Brazilian Journal of Physics 43(3) (2013), 182-198.
Igor Podlubný, Fractional Differential Equations, Academic Press, United States, 1998.
H. D. Wahlquist and F. B. Estabrook, Bäcklund transformation for solutions of the Korteweg-de Vries equation, Phys. Rev. Lett. 31 (1973), 1386-1390.
A. M. Wazwaz, A reliable technique for solving linear and nonlinear Schrodinger equations by Adomian decomposition method, BIMAS 29(2) (2001), 125-134.
Hans J. Wospakrik and Freddy P. Zen, Inhomogeneous Burgers equation and the Feynman-Kac path integral, 1998.
https://doi.org/10.48550/arXiv.solv-int/9812014.
Gérard Zongo, Ousséni So, Geneviève Barro, Youssouf Paré and Blaise Somé, A comparison of Adomian’s method and SBA method on the nonlinear Schrödinger’s equation, Far East J. Dyn. Syst. 29(4) (2017), 149-161.
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