حل عددي لمعادلة فريدهولم التفاضلية التكاملية الخطية باستخدام متعددة حدود تشارد.
الشريط الجانبي للمقالة
محتوى المقالة الرئيسي
الملخص
تم تقديم طريقة جديدة تستند الى متعددة حدود تشارد للحل العددي لمعادلات فريدهولم التفاضلية التكاملية من المرتبة الاولى والنوع الثاني مع الشرط. تم الحصول ببساطة على مشتقة متعددة حدود تشارد وتكاملها. واعطيت دقة الطريقة المقدمة وثبتت قابلية تطبيقها ببعض الامثلة العددية. تتم مقارنة النتائج التي تم الحصول عليها مع النتائج المعروفة الاخرى.
Received 25/1/2020, Accepted 4/6/2020, Published Online First 11/1/2021
تفاصيل المقالة
هذا العمل مرخص بموجب Creative Commons Attribution 4.0 International License.
كيفية الاقتباس
المراجع
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