A novel variant of a product integration method and its relation to discrete fractional calculus

2017 ◽  
Vol 114 ◽  
pp. 179-187 ◽  
Author(s):  
S. McKee ◽  
Jose A. Cuminato
Keyword(s):  
Fractional Calculus ◽  
Integration Method ◽  
Discrete Fractional Calculus ◽  
Product Integration ◽  
Novel Variant ◽  
Product Integration Method

scholarly journals Numerical Techniques for Solving Linear Volterra Fractional Integral Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Safa’ Hamdan ◽  
Naji Qatanani ◽  
Adnan Daraghmeh
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Fractional Integral ◽  
Integration Method ◽  
Haar Wavelet ◽  
Numerical Techniques ◽  
Product Integration ◽  
Fractional Integral Equation ◽  
Product Integration Method ◽  
Good Agreement

Two numerical techniques, namely, Haar Wavelet and the product integration methods, have been employed to give an approximate solution of the fractional Volterra integral equation of the second kind. To test the applicability and efficiency of the numerical method, two illustrative examples with known exact solution are presented. Numerical results show clearly that the accuracy of these methods are in a good agreement with the exact solution. A comparison between these methods shows that the product integration method provides more accurate results than its counterpart.

scholarly journals AN EXTENSION OF THE PRODUCT INTEGRATION METHOD TO L1 WITH APPLICATIONS IN ASTROPHYSICS

2016 ◽  
Vol 21 (6) ◽  
pp. 774-793 ◽  
Author(s):  
Laurence Grammont ◽  
Mario Ahues ◽  
Hanane Kaboul
Keyword(s):  
Integral Equation ◽  
Existence And Uniqueness ◽  
Integration Method ◽  
Sufficient Conditions ◽  
Iterative Refinement ◽  
Weakly Singular Kernel ◽  
Product Integration ◽  
Weakly Singular ◽  
Uniqueness Of The Solution ◽  
Product Integration Method

A Fredholm integral equation of the second kind in L1([a, b], C) with a weakly singular kernel is considered. Sufficient conditions are given for the existence and uniqueness of the solution. We adapt the product integration method proposed in C0 ([a, b], C) to apply it in L1 ([a, b], C), and discretize the equation. To improve the accuracy of the approximate solution, we use different iterative refinement schemes which we compare one to each other. Numerical evidence is given with an application in Astrophysics.

An adapted integration method for Volterra integral equation of the second kind with weakly singular kernel

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ahlem Nemer ◽  
Hanane Kaboul ◽  
Zouhir Mokhtari
Keyword(s):  
Integral Equation ◽  
Integration Method ◽  
New Product ◽  
Linear Interpolation ◽  
Weakly Singular Kernel ◽  
Product Integration ◽  
Weakly Singular ◽  
Product Integration Method ◽  
Singular Kernels ◽  
Linear Volterra Integral Equations

Abstract In this paper, we consider general cases of linear Volterra integral equations under minimal assumptions on their weakly singular kernels and introduce a new product integration method in which we involve the linear interpolation to get a better approximate solution, figure out its effect and also we provide a convergence proof. Furthermore, we apply our method to a numerical example and conclude this paper by adding a conclusion

Product integration method for simulation of radial effects in dry spinning processes

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Manuel Wieland ◽  
Walter Arne ◽  
Robert Feßler ◽  
Nicole Marheineke ◽  
Raimund Wegener
Keyword(s):  
Integration Method ◽  
Product Integration ◽  
Dry Spinning ◽  
Product Integration Method
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