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Modified variational iteration technique for solving singular fourth-order parabolic partial differential equations. (English) Zbl 1238.65103

Summary: We apply the modified variational iteration method to solving singular fourth-order parabolic partial differential equations. The proposed modification is made by introducing He’s polynomials into the correct functional. The developed algorithm is quite efficient and is well suited practically for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the suggested method. The fact that the modified variational iteration method (MVIM) solves nonlinear problems without using the Adomian’s polynomials can be considered as a clear advantage of this technique over the decomposition method.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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