Approximate solution of nonlinear differential equations with convolution product nonlinearities. (English) Zbl 0932.65143

He, Jihuan

Comput. Methods Appl. Mech. Eng. 167, No. 1-2, 69-73 (1998).

Summary: A new iteration method is proposed to solve nonlinear problems. Special attention is paid to nonlinear differential equations with convolution product nonlinearities. The results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems. Furthermore, the first-order approximations are more accurate than perturbation solutions at high-order approximation.

MSC:

65R20	Numerical methods for integral equations
45J05	Integro-ordinary differential equations
45G10	Other nonlinear integral equations

Keywords:

nonlinear integro-ordinary differential equations; variational iteration method; Lagrange multiplier method; nonlinear differential equations with convolution product nonlinearities

References:

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