scholarly journals An Efficient Numerical Method for Solving Volterra-Fredholm Integro-Differential Equations of Fractional Order by Using Shifted Jacobi-Spectral Collocation Method

2018 ◽  
Vol 15 (3) ◽  
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Collocation Method ◽  
Fractional Order ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Jacobi Spectral Collocation Method

scholarly journals An Efficient Numerical Method for a Class of Nonlinear Volterra Integro-Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
M. H. Daliri Birjandi ◽  
J. Saberi-Nadjafi ◽  
A. Ghorbani
Keyword(s):  
Differential Equations ◽  
Convergence Rate ◽  
Numerical Method ◽  
Collocation Method ◽  
Nonlinear Equations ◽  
Iteration Method ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Modified Method ◽  
Computational Work

We investigate an efficient numerical method for solving a class of nonlinear Volterra integro-differential equations, which is a combination of the parametric iteration method and the spectral collocation method. The implementation of the modified method is demonstrated by solving several nonlinear Volterra integro-differential equations. The results reveal that the developed method is easy to implement and avoids the additional computational work. Furthermore, the method is a promising approximate tool to solve this class of nonlinear equations and provides us with a convenient way to control and modify the convergence rate of the solution.

scholarly journals Shifted Jacobi spectral collocation method with convergence analysis for solving integro-differential equations and system of integro-differential equations

2019 ◽  
Vol 24 (3) ◽  
pp. 332-352 ◽  
Author(s):  
Eid H. Doha ◽  
Mohamed A. Abdelkawy ◽  
Ahmed Z.M. Amin ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Jacobi Polynomials ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Numerical Examples ◽  
Shifted Jacobi Polynomials ◽  
Present Technique ◽  
Jacobi Spectral Collocation Method ◽  
The Given

This article addresses the solution of multi-dimensional integro-differential equations (IDEs) by means of the spectral collocation method and taking the advantage of the properties of shifted Jacobi polynomials. The applicability and accuracy of the present technique have been examined by the given numerical examples in this paper. By means of these numerical examples, we ensure that the present technique is simple and very accurate. Furthermore, an error analysis is performed to verify the correctness and feasibility of the proposed method when solving IDE.

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