Numerical solution of nonlinear two-dimensional Volterra integral equation of the second kind in the reproducing kernel space

In this article, an effective method is given to solve nonlinear two-dimensional Volterra integral equations of the second kind. First, we find the solution of integral equation in terms of reproducing kernel functions in series, then by truncating the series an approximate solution obtained. In add...

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Bibliographic Details
Published in:Mathematical sciences (Karaj, Iran) Iran), 2017-06, Vol.11 (2), p.139-144
Main Authors: Fazli, A., Allahviranloo, T., Javadi, Sh
Format: Article
Language:English
Subjects:
Applications of Mathematics
Integral equations
Kernel functions
Mathematics
Mathematics and Statistics
Nonlinear equations
Original Research
Volterra integral equations
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Summary:In this article, an effective method is given to solve nonlinear two-dimensional Volterra integral equations of the second kind. First, we find the solution of integral equation in terms of reproducing kernel functions in series, then by truncating the series an approximate solution obtained. In addition, the calculation of Fourier coefficients solution of the integral equation in terms of reproducing kernel functions is notable. Numerical examples are presented, and their results are compared with the analytical solution to demonstrate the validity and applicability of the method.
ISSN:2008-1359
2251-7456
DOI:10.1007/s40096-017-0219-z