##
**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 |

### Keywords:

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

\textit{J. He}, Comput. Methods Appl. Mech. Eng. 167, No. 1--2, 69--73 (1998; Zbl 0932.65143)

Full Text:
DOI

### References:

[1] | He, J. H., A new approach to nonlinear partial differential equations, Comm. Nonlinear Sci. Numer. Simul., 2, 4, 230-235 (1997) · Zbl 0923.35046 |

[2] | He, J. H., A variational iteration approach to nonlinear problems and its application, Mech. Applic., 20, 1, 30-31 (1998) |

[3] | J.H. He, Variational iteration method: A new approach to nonlinear analytical technique, J. Shanghai Mech. to appear.; J.H. He, Variational iteration method: A new approach to nonlinear analytical technique, J. Shanghai Mech. to appear. |

[4] | Inokuti, M., General use of the Lagrange multiplier in nonlinear mathematical physics, (Nemat-Nassed, S., Variational Method in the Mechanics of Solids (1978), Pergamon Press), 156-162 |

[5] | Finlayson, B. A., The Method of Weighted Residuals and Variational Principles (1972), Academic Press · Zbl 0319.49020 |

[6] | Adomian, G.; Roch, R., On the solution of nonlinear differential equations with convolution product nonlinearities, J. Math. Anal. Appl., 114, 171-175 (1986) · Zbl 0588.34004 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.