Block collocation boundary value solutions of the first-kind Volterra integral equations

2020 ◽  
Author(s):  
Ling Liu ◽  
Junjie Ma
Keyword(s):  
Integral Equations ◽  
Boundary Value ◽  
Volterra Integral Equations

scholarly journals Fractal boundary value problems for integral and differential equations with local fractional operators

2015 ◽  
Vol 19 (3) ◽  
pp. 959-966 ◽  
Author(s):  
Xiao-Jun Yang ◽  
Dumitru Baleanub ◽  
Mihailo Lazarevic ◽  
Milan Cajic
Keyword(s):  
Heat Conduction ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Decomposition Method ◽  
Wave Equations ◽  
Boundary Value ◽  
Volterra Integral Equations ◽  
Fractional Operators ◽  
Fractal Boundary

In the present paper we investigate the fractal boundary value problems for the Fredholm\Volterra integral equations, heat conduction and wave equations by using the local fractional decomposition method. The operator is described by the local fractional operators. The four illustrative examples are given to elaborate the accuracy and reliability of the obtained results.

scholarly journals Superconvergence of interpolated collocation solutions for weakly singular Volterra integral equations of the second kind

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Qiumei Huang ◽  
Min Wang
Keyword(s):  
Integral Equations ◽  
Numerical Experiments ◽  
Volterra Integral Equations ◽  
Least Square ◽  
Convergence Order ◽  
Collocation Points ◽  
Weakly Singular ◽  
Interpolation Postprocessing ◽  
Collocation Solution

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.

A stochastic operational matrix method for numerical solutions of multi-dimensional stochastic Itô–Volterra integral equations

2020 ◽  
Vol 28 (3) ◽  
pp. 209-216
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix ◽  
Block Pulse Function

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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