COMPARISON OF THREE NUMERICAL ANALYSIS METHODS ON A LINEAR SECOND KIND FREDHOLM INTEGRO-DIFFERENTIAL EQUATION

2021 ◽  
Vol 25 (1) ◽  
pp. 1-10
Author(s):  
Ouedraogo Seny ◽  
Bassono Francis ◽  
Yaro Rasmane ◽  
Youssouf Pare
Keyword(s):  
Differential Equation ◽  
Numerical Analysis ◽  
Integro Differential Equation ◽  
Analysis Methods

scholarly journals Numerical analysis of a method for a partial integro-differential equation model in regulatory gene networks

2018 ◽  
Vol 28 (10) ◽  
pp. 2069-2095 ◽  
Author(s):  
Antonio A. Alonso ◽  
Rodolfo Bermejo ◽  
Manuel Pájaro ◽  
Carlos Vázquez
Keyword(s):  
Differential Equation ◽  
Numerical Analysis ◽  
Gene Networks ◽  
Regulatory Networks ◽  
Regulatory Gene ◽  
Spatial Dimension ◽  
Equation Model ◽  
Lagrangian Method ◽  
Second Order ◽  
Integro Differential Equation

In this paper, we propose a semi-Lagrangian Runge–Kutta method to approximate the solution of a multidimensional partial integro-differential equation (PIDE) model for regulatory networks involving multiple genes with self- and cross-regulations. For the first time in the literature, we address the numerical analysis of a semi-Lagrangian method for a PIDE model without second-order derivative terms. From this analysis, we obtain second-order convergence in time and space. Moreover, some examples with analytical solution in one spatial dimension illustrate the theoretical results, while others in higher dimensions show the expected behavior of the solution. Finally, the scalability of the method and the comparison with a previously proposed first-order semi-Lagrangian method are discussed.

Some numerical graphs with successive approximation method of fractional integro–differential equation

2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas
Keyword(s):  
Differential Equation ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Integro Differential Equation

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].

Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

2018 ◽  
pp. 491
Author(s):  
Abdul Khaleq O. Al-Jubory ◽  
Shaymaa Hussain Salih
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Bernstein Basis ◽  
Traditional Methods ◽  
Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

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