scholarly journals SOLVING NONLINEAR FRACTIONAL VOLTERRA INTEGRAL EQUATIONS OF SECOND KIND BY THE ADOMIAN METHOD

2022 ◽  
Vol 29 (1) ◽  
pp. 97-110
Author(s):  
Ouedraogo Seny ◽  
Justin Mouyedo Loufouilou ◽  
Bonazebi Yindoula Joseph ◽  
Youssouf Pare
2005 ◽  
Vol 161 (3) ◽  
pp. 745-751 ◽  
Author(s):  
H. Sadeghi Goghary ◽  
Sh. Javadi ◽  
E. Babolian

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Qiumei Huang ◽  
Min Wang

AbstractIn this paper, we discuss the superconvergence of the “interpolated” collocation solutions for weakly singular Volterra integral equations of the second kind. Based on the collocation solution $$u_h$$ u h , two different interpolation postprocessing approximations of higher accuracy: $$I_{2h}^{2m-1}u_h$$ I 2 h 2 m - 1 u h based on the collocation points and $$I_{2h}^{m}u_h$$ I 2 h m u h based on the least square scheme are constructed, whose convergence order are the same as that of the iterated collocation solution. Such interpolation postprocessing methods are much simpler in computation. We further apply this interpolation postprocessing technique to hybrid collocation solutions and similar results are obtained. Numerical experiments are shown to demonstrate the efficiency of the interpolation postprocessing methods.


2020 ◽  
Vol 28 (3) ◽  
pp. 209-216
Author(s):  
S. Singh ◽  
S. Saha Ray

AbstractIn this article, hybrid Legendre block-pulse functions are implemented in determining the approximate solutions for multi-dimensional stochastic Itô–Volterra integral equations. The block-pulse function and the proposed scheme are used for deriving a methodology to obtain the stochastic operational matrix. Error and convergence analysis of the scheme is discussed. A brief discussion including numerical examples has been provided to justify the efficiency of the mentioned method.


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