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Numerical solution of Burgers equation by the Sobolev gradient method. (English) Zbl 1415.65241

Summary: Burgers’ equation is solved numerically with Sobolev gradient methods. A comparison is shown with other numerical schemes presented in this journal, such as modified Adomian method (MAM) [S. Abbasbandy and M.T. Darvishi, Appl. Math. Comput. 163, No. 3, 1265–1272 (2005; Zbl 1060.65649)] and by a variational method (VM) which is based on the method of discretization in time [E. N. Aksan and A. Özdes, Appl. Math. Comput. 156, No. 2, 395–402 (2004; Zbl 1061.65085)]. It is shown that the Sobolev gradient methods are highly efficient while at the same time retaining the simplicity of steepest descent algorithms.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35Q55 NLS equations (nonlinear Schrödinger equations)
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