Approximate solutions for nonlinear initial value problems using the modified variational iteration method. (English) Zbl 1251.65148

Nofal, Taher A.

J. Appl. Math. 2012, Article ID 370843, 19 p. (2012).

Summary: We use the modified variational iteration method (MVIM) to find the approximate solutions for some nonlinear initial value problems in the mathematical physics, via the Burgers-Fisher equation, the Kuramoto-Sivashinsky equation, the coupled Schrödinger-KdV equations, and the long-short wave resonance equations together with initial conditions. The results of these problems reveal that the modified variational iteration method is very powerful, effective, convenient, and quite accurate to systems of nonlinear equations. It is predicted that this method can be found widely applicable in engineering and physics.

MSC:

65M99	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35Q55	NLS equations (nonlinear Schrödinger equations)
35Q53	KdV equations (Korteweg-de Vries equations)

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