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The Approximate Solution of Nonlinear Integral Equations with the RH Wavelet Bases in a Complex Plane

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Abstract

This study has been conducted to calculate the one-dimensional nonlinear Volterra–Fredholm and mixed Volterra–Fredholm integral equation of second kind in a complex plane, regarding the use of the wavelet. As far as we are aware, there have been no studies conducted so far to solve this kind of integral equation in the complex plane. The main feature of this method is that, it approximates the integral equations without solving any linear or algebra systems. In “Approximation of the Solutions with RH Functions” section, the integral operator for the RH wavelet and its use will be presented in our numerical methods. “Error Analysis” section, will discuss about the unique solution of the mentioned problems. Furthermore, an upper bound for the error analysis will be given. Finally, some problem examples and their solution will be proposed in “Numerical Examples” section.

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  1. Department of Science, School of Mathematical Sciences, University of Zabol, Zabol, Iran

    M. Erfanian

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  1. M. Erfanian
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Correspondence to M. Erfanian.

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Erfanian, M. The Approximate Solution of Nonlinear Integral Equations with the RH Wavelet Bases in a Complex Plane. Int. J. Appl. Comput. Math 4, 31 (2018). https://doi.org/10.1007/s40819-017-0465-7

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  • DOI: https://doi.org/10.1007/s40819-017-0465-7

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