Solving the nonlinear integro-differential equation in complex plane with rationalized Haar wavelet

Majid Erfanian and Amin Mansoori

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 165, issue C, 223-237

Abstract: We investigate mixed nonlinear integro-differential equations (MNIDEs) in general, utilizing the concept of rationalized Haar (RH) wavelet. The complexity of the MNIDE solution is known to everyone. For this purpose, we present a numerical method by applying the RH wavelet to approximate solutions of the MNIDE of the second kind in the complex plane. At first, we describe a continuous integral operator . Also, under mild assumptions, the Banach fixed point theorem ensures that the integral operator has a unique solution. Moreover, we give a result for error and compute the rate of convergence. Employing an algorithm, we present some illustrative examples to demonstrate the performance of this approach.

Keywords: Nonlinear integro-differential equation; Rationalized Haar wavelet; Fixed point theorem; Complex plane (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:165:y:2019:i:c:p:223-237

DOI: 10.1016/j.matcom.2019.03.006

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