scholarly journals A Novel Method for Solving Nonlinear Volterra Integro-Differential Equation Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Mohammad Hossein Daliri Birjandi ◽  
Jafar Saberi-Nadjafi ◽  
Asghar Ghorbani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Iteration Method ◽  
Spectral Collocation ◽  
Numerical Examples ◽  
Integro Differential Equation ◽  
Collocation Technique ◽  
Computational Work ◽  
Novel Method

An efficient iteration method is introduced and used for solving a type of system of nonlinear Volterra integro-differential equations. The scheme is based on a combination of the spectral collocation technique and the parametric iteration method. This method is easy to implement and requires no tedious computational work. Some numerical examples are presented to show the validity and efficiency of the proposed method in comparison with the corresponding exact solutions.

Numerical solution of the general Volterra nth-order integro-differential equations via variational iteration method

2018 ◽  
Vol 13 (02) ◽  
pp. 2050042
Author(s):  
Fernane Khaireddine
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Numerical Solution ◽  
General Formula ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Linear And Nonlinear

In this paper, we use the variational iteration method (VIM) to construct approximate solutions for the general [Formula: see text]th-order integro-differential equations. We show that his method can be effectively and easily used to solve some classes of linear and nonlinear Volterra integro-differential equations. Finally, some numerical examples with exact solutions are given.

scholarly journals An Efficient Numerical Method for a Class of Nonlinear Volterra Integro-Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
M. H. Daliri Birjandi ◽  
J. Saberi-Nadjafi ◽  
A. Ghorbani
Keyword(s):  
Differential Equations ◽  
Convergence Rate ◽  
Numerical Method ◽  
Collocation Method ◽  
Nonlinear Equations ◽  
Iteration Method ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Modified Method ◽  
Computational Work

We investigate an efficient numerical method for solving a class of nonlinear Volterra integro-differential equations, which is a combination of the parametric iteration method and the spectral collocation method. The implementation of the modified method is demonstrated by solving several nonlinear Volterra integro-differential equations. The results reveal that the developed method is easy to implement and avoids the additional computational work. Furthermore, the method is a promising approximate tool to solve this class of nonlinear equations and provides us with a convenient way to control and modify the convergence rate of the solution.

scholarly journals Formulation and Solution of th-Order Derivative Fuzzy Integrodifferential Equation Using New Iterative Method with a Reliable Algorithm

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
A. A. Hemeda
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Integrodifferential Equation ◽  
Order Derivative ◽  
Parametric Form ◽  
Numerical Examples ◽  
Integro Differential Equation ◽  
New Iterative Method

Thenth-order derivative fuzzy integro-differential equation in parametric form is converted to its crisp form, and then the new iterative method with a reliable algorithm is used to obtain an approximate solution for this crisp form. The analysis is accompanied by numerical examples which confirm efficiency and power of this method in solving fuzzy integro-differential equations.

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.   

Legendre Spectral Collocation Technique for Advection Dispersion Equations Included Riesz Fractional

2021 ◽  
Vol 6 (1) ◽  
pp. 9
Author(s):  
Mohamed M. Al-Shomrani ◽  
Mohamed A. Abdelkawy
Keyword(s):  
Numerical Methods ◽  
Numerical Algorithm ◽  
Spectral Collocation ◽  
Theoretical Formulation ◽  
Numerical Examples ◽  
Dispersion Equations ◽  
Advection Dispersion ◽  
Collocation Technique ◽  
Collocation Approach

The advection–dispersion equations have gotten a lot of theoretical attention. The difficulty in dealing with these problems stems from the fact that there is no perfect answer and that tackling them using local numerical methods is tough. The Riesz fractional advection–dispersion equations are quantitatively studied in this research. The numerical methodology is based on the collocation approach and a simple numerical algorithm. To show the technique’s performance and competency, a comprehensive theoretical formulation is provided, along with numerical examples.

scholarly journals Sinc-Galerkin method for solving hyperbolic partial differential equations

2018 ◽  
Vol 8 (2) ◽  
pp. 250-258 ◽  
Author(s):  
Aydin Secer
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solutions ◽  
Galerkin Method ◽  
Hyperbolic Equations ◽  
Approximate Solutions ◽  
Equation System ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential ◽  
Numerical Examples

In this work, we consider the hyperbolic equations to determine the approximate solutions via Sinc-Galerkin Method (SGM). Without any numerical integration, the partial differential equation transformed to an algebraic equation system. For the numerical calculations, Maple is used. Several numerical examples are investigated and the results determined from the method are compared with the exact solutions. The results are illustrated both in the table and graphically.

The approximate solution of nonlinear Fredholm implicit integro-differential equation in the complex plane

2021 ◽  
Author(s):  
Samir Lemita ◽  
Sami Touati ◽  
Kheireddine Derbal
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Approximate Solution ◽  
Integral Operator ◽  
Complex Plane ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Integro Differential Equation ◽  
Numerical Process

This paper’s purpose is to study the nonlinear Fredholm implicit integro-differential equation in the complex plane, where the term implicit integro-differential means that the derivative of unknown function is founded inside of the integral operator. Initially, according to Banach fixed point theory, we ensure that the equation has a unique solution under particular conditions. However, we exhibit a numerical process based on the conjunction between Nyström and Picard methods, for the sake of approximating solutions of this equation. In addition to that, the convergence analysis of this numerical process is demonstrated, and some illustrated numerical examples are presented.

On the physical and mathematical interpretation of the isokinetic hypothesis

2004 ◽  
Vol 120 ◽  
pp. 85-91
Author(s):  
T. Reti
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Special Property ◽  
State Parameter ◽  
Temperature History ◽  
Temperature Function ◽  
Integro Differential Equation ◽  
Right Hand ◽  
Mathematical Interpretation ◽  
State Functions

Based on the investigation of additive kinetic differential equations it is shown that the concept of the traditional isokinetic hypothesis defined by Christian can be easily generalized. By introducing the notion of the weakly isokinetic process, it is verified that the extended isokinetic model can be expressed in terms of an integro-differential equation. A special property of this integro-differential equation is that its right-hand side includes such state-parameters, which are determined by the whole temperature history (i.e. each state parameter is a functional of the time-temperature function, or any other selected state functions).

scholarly journals ASYMPTOTIC EXPANSION OF SOLUTION OF GENERAL BVP WITH INITIAL JUMPS FOR HIGHER-ORDER SINGULARLY PERTURBED INTEGRO-DIFFERENTIAL EQUATION

2018 ◽  
pp. 28-36
Author(s):  
Dauylbayev M. ◽  
Atakhan N. ◽  
Mirzakulova A.E.
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansion ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Higher Order ◽  
Singularly Perturbed ◽  
Jump Phenomenon ◽  
Integro Differential Equation ◽  
Asymptotic Expansion Of Solution ◽  
Initial Jump

In this article we constructed an asymptotic expansion of the solution undivided boundary value problem for singularly perturbed integro-differential equations with an initial jump phenomenon m – th order. We obtain the theorem about estimation of the remainder term’s asymptotic with any degree of accuracy in the smallparameter.

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