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