On numerical solution of two-dimensional nonlinear Urysohn fuzzy integral equations based on fuzzy Haar wavelets

2017 ◽  
Vol 309 ◽  
pp. 145-164 ◽  
Author(s):  
R. Ezzati ◽  
S.M. Sadatrasoul
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Haar Wavelets ◽  
Fuzzy Integral ◽  
Two Dimensional

Solving systems of fractional two-dimensional nonlinear partial Volterra integral equations by using Haar wavelets

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Amir Ahmad Khajehnasiri ◽  
R. Ezzati ◽  
M. Afshar Kermani
Keyword(s):  
Nonlinear System ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Fractional Integration ◽  
Volterra Integral Equations ◽  
Haar Wavelets ◽  
Operational Matrices ◽  
Two Dimensional ◽  
Numerical Examples

Abstract The main aim of this paper is to use the operational matrices of fractional integration of Haar wavelets to find the numerical solution for a nonlinear system of two-dimensional fractional partial Volterra integral equations. To do this, first we present the operational matrices of fractional integration of Haar wavelets. Then we apply these matrices to solve systems of two-dimensional fractional partial Volterra integral equations (2DFPVIE). Also, we present the error analysis and convergence as well. At the end, some numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.

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