Numerical Solution for Linear Fredholm Integro-Differential Equation Using Touchard Polynomials

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Jalil Talab Abdullah

Abstract

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.


 

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Abdullah JT. Numerical Solution for Linear Fredholm Integro-Differential Equation Using Touchard Polynomials. Baghdad Sci.J [Internet]. 2021Jun.1 [cited 2021Dec.4];18(2):0330. Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/4769
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References

Wazwaz A. M. Linear and Nonlinear Integral Equations Methods and Applications. Springer Berlin, Heidelberg; 2011. 33-38 p.

Dzhumabaev D. S. New general solutions to linear Fredholm integro-differential equations and their applications on solving the boundary value problems. J. Comput Appl. Math. 2018 Jan. 1; 327: 79-108.

Biçer G. G, Öztürk Y, Gülsu M. Numerical approach for solving linear Fredholm integro-differential equation with piecewise intervals by Bernoulli polynomials. IJCM. 2018; 95(10): 2100-2111.

S. Davaeifar, J. Rashidinia, M. Amirfakhrian. Bernstein Polynomial Approach for Solution of Higher-Order Mixed Linear Fredholm Integro-Differential-Difference Equations with Variable Coefficients. TWMS J. Pure Appl. Math. 2016; 7(1): 46-62

Dzhumabaev D. S. On One Approach to Solve the Linear Boundary Value Problems for Fredholm Integro-Differential Equations. J. Comput. Appl. Math. 2016 March. 1; 294: 342-357.

Du H, Zhao G, Zhao C. Reproducing Kernel Method for Solving Fredholm Integro-Differential Equations with Weakly singularity. J. Comput. Appl. Math. 2014 Jan. 1; 255 (2014): 122-132.

R. Jalilian, T. Tahernezhad. Exponential Spline Method for Approximation Solution of Fredholm Integro-Differential Equation. IJCM. 2019 Feb 18; 97(4): 791-801.

https://doi.org/10.1080/00207160.2019.1586891

Xue Q, Niu J, Yu D, Ran C. An Improved Reproducing Kernel Method for Fredholm Integro-Differential Type Two-Point Boundary Value Problems. IJCM. 2018; 95(5): 1015-1023

Fairbairn A. I, Kelmanson M. A. A priori Nyström-Method Error Bounds in Approximate Solutions of 1-D Fredholm Integro-Differential Equations. IJMS. 2018 Nov 6; 150 (2019): 755– 766.

Kurt A, Yalçınbaş S, Sezer M. Fibonacci Collocation Method for Solving High-Order Linear Fredholm Integro-Differential-Difference Equations. Math. comput. appl. 2013 Jun; 18(3):448-458.

Available from: https://doi.org/10.1155/2013/486013

Berenguer M. I, Muñoz M. F, Garralda-Guillem A. I, Galán M. R. A sequential Approach for Solving the Fredholm Integro-Differential Equation. Appl. Numer. Math. 2012; 62(2012): 297–304

Nazir A, Usman M, Mohyud-Din S. T. Tauseef Mohyud-din.Touchard Polynomials Method for Integral Equations. Int. J. Modern Theo. Physics. 2017 Aug 30; 3(1): 74-89.

Paris R. B. The Asymptotes of the Touchard Polynomials: A Uniform Approximation. Mathematica Aeterna. 2016 Jun 28; 6(5): 765-779.

Mihoubi M, Maamra M. S.Touchard Polynomials, Partial Bell Polynomials and Polynomials of Binomial Type. J. Integer Seq. 2011 Mar 25; 14(2011): 1-9.

Yasmin G. Some Identities of the Apostol Type Polynomials Arising From Umbral Calculus. PJM. 2018; 7(1): 35-52

Danfu H, Xufeng S. Numerical Solution of Integro-Differential Equations by Using CAS Wavelet Operational Matrix of Integration. App. Math. Comput. 2007 Dec 15; 194(2): 460-466. Available from:https://doi.org/10.1016/j.amc.2007.04.048

Darania P, Ebadian A. A Method for the Numerical Solution of the Integro-Differential Equations. Appl. Math. Comput [Internet]. 2007 May 1; 188(1): 657-668. https://doi.org/10.1016/j.amc.2006.10.046

Dehghan M, Salehi R.The Numerical Solution of the Non-Linear Integro-Differential Equations Based on The Mesh Less Method. J. Comput. Appl. Math. 2012; 236(9): 2367-2377. https://doi.org/10.1016/j.cam.2011.11.022