On the numerical solution of a class of linear fractional integro-differential algebraic equations with weakly singular kernels

2019 ◽  
Vol 144 ◽  
pp. 1-20 ◽  
Author(s):  
F. Ghanbari ◽  
P. Mokhtary ◽  
K. Ghanbari
Keyword(s):  
Numerical Solution ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Singular Kernels

scholarly journals Matrix Method by Genocchi Polynomials for Solving Nonlinear Volterra Integral Equations with Weakly Singular Kernels

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2105
Author(s):  
Elham Hashemizadeh ◽  
Mohammad Ali Ebadi ◽  
Samad Noeiaghdam
Keyword(s):  
Integral Equations ◽  
Operational Matrix ◽  
Volterra Integral Equations ◽  
Group Symmetry ◽  
Algebraic Equations ◽  
Weakly Singular Kernels ◽  
Euler’S Method ◽  
Genocchi Polynomials ◽  
Weakly Singular ◽  
Singular Kernels

In this study, we present a spectral method for solving nonlinear Volterra integral equations with weakly singular kernels based on the Genocchi polynomials. Many other interesting results concerning nonlinear equations with discontinuous symmetric kernels with application of group symmetry have remained beyond this paper. In the proposed approach, relying on the useful properties of Genocchi polynomials, we produce an operational matrix and a related coefficient matrix to convert nonlinear Volterra integral equations with weakly singular kernels into a system of algebraic equations. This method is very fast and gives high-precision answers with good accuracy in a low number of repetitions compared to other methods that are available. The error boundaries for this method are also presented. Some illustrative examples are provided to demonstrate the capability of the proposed method. Also, the results derived from the new method are compared to Euler’s method to show the superiority of the proposed method.

scholarly journals A note on orthogonal polynomials

1970 ◽  
Vol 17 (1) ◽  
pp. 83-94 ◽  
Author(s):  
D. Kershaw
Keyword(s):  
Orthogonal Polynomials ◽  
Numerical Solution ◽  
Integral Equations ◽  
Fredholm Integral Equations ◽  
Intermediate Result ◽  
Weakly Singular Kernels ◽  
Quadrature Formulae ◽  
Weakly Singular ◽  
Gauss Type ◽  
Singular Kernels

During an investigation into the existence of Gauss-type quadrature formulae for the numerical solution of Fredholm integral equations with weakly singular kernels an intermediate result was found which is of independent interest.

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