The combined reproducing kernel method and Taylor series for handling nonlinear Volterra integro-differential equations with derivative type kernel

The reproducing kernel method is applied to Volterra nonlinear integro-differential equations. In this technique, the nonlinear term is replaced by its Taylor series. The exact solution is represented in the form of series in the reproducing Hilbert kernel space. The approximation solution is expres...

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Bibliographic Details
Published in:Applied mathematics and computation 2019-08, Vol.355, p.151-160
Main Authors: Alvandi, Azizallah, Paripour, Mahmoud
Format: Article
Language:English
Subjects:
Reproducing kernel method
Taylor series
Volterra nonlinear integro-differential equation
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Summary:The reproducing kernel method is applied to Volterra nonlinear integro-differential equations. In this technique, the nonlinear term is replaced by its Taylor series. The exact solution is represented in the form of series in the reproducing Hilbert kernel space. The approximation solution is expressed by n-term summation of reproducing kernel functions. Some numerical examples are solved in two different spaces and parameters of n. Measurements of the experimental data is an indications of stability and convergence on the reproducing kernel.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2019.02.023