scholarly journals Reliable Iterative Method for solving Volterra - Fredholm Integro Differential Equations

2021 ◽  
Vol 26 (2) ◽  
Author(s):  
Samaher Marez
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Iterative Process ◽  
Initial Conditions ◽  
High Accuracy ◽  
Series Solutions ◽  
Math Program ◽  
The Right

  The aim of this paper, a reliable iterative method is presented for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method.  Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibit that this technique has compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

scholarly journals The Laplace-Adomian-Pade Technique for the ENSO Model

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Yi Zeng
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Initial Conditions ◽  
Approximate Solutions ◽  
Decomposition Methods ◽  
High Accuracy ◽  
Padé Method

The Laplace-Adomian-Pade method is used to find approximate solutions of differential equations with initial conditions. The oscillation model of the ENSO is an important nonlinear differential equation which is solved analytically in this study. Compared with the exact solution from other decomposition methods, the approximate solution shows the method’s high accuracy with symbolic computation.

scholarly journals Numerical Solution of Non-linear Delay Differential Equations Using Semi Analytic Iterative Method

2019 ◽  
Vol 25 (103) ◽  
pp. 131-142
Author(s):  
Asmaa A. Aswhad ◽  
Samaher M. Yassein
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Iterative Method ◽  
Numerical Solution ◽  
Delay Differential Equations ◽  
Initial Conditions ◽  
Linear Delay ◽  
Non Linear ◽  
Delay Differential

       We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.                       

scholarly journals Application of Iterative Method for Solving Higher Order Integro-Differential Equations

2019 ◽  
Vol 32 (2) ◽  
pp. 51 ◽  
Author(s):  
Samaher M. Yassein
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Numerical Methods ◽  
Differential Equations ◽  
Iterative Method ◽  
Convergent Series ◽  
Higher Order ◽  
Series Solutions ◽  
Solution Series ◽  
A New Technique

The main aim of this paper is to apply a new technique suggested by Temimi and Ansari namely (TAM) for solving higher order Integro-Differential Equations. These equations are commonly hard to handle analytically so it is request numerical methods to get an efficient approximate solution. Series solutions of the problem under consideration are presented by means of the Iterative Method (IM). The numerical results show that the method is effective, accurate and easy to implement rapidly convergent series to the exact solution with minimum amount of computation. The MATLAB is used as a software for the calculations.           

Systems of Nonlinear Fractional Differential Equations

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Unique Solution ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
The Right ◽  
Linear Fractional Differential Equations

AbstractUsing the iterative method, this paper investigates the existence of a unique solution to systems of nonlinear fractional differential equations, which involve the right-handed Riemann-Liouville fractional derivatives $D^{q}_{T}x$ and $D^{q}_{T}y$. Systems of linear fractional differential equations are also discussed. Two examples are added to illustrate the results.

scholarly journals APPROXIMATE SOLUTIONS OF SOME NONLINEAR PROBLEMS FOR THE MONGE-AMPERE EQUATIO

2020 ◽  
pp. 97-105
Author(s):  
N.B. Iskakova ◽  
◽  
А.S. Rysbek ◽  
N.S. Serik ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Initial Conditions ◽  
Boundary Value ◽  
Nonlinear Problems ◽  
Approximate Solutions ◽  
Mathcad Software ◽  
The Right ◽  
Monge Ampere

Due to numerous applications in various fields of science, including gas dynamics, meteorology, differential geometry, and others, the Monge – ampere equation is one of the most intensively studied equations of nonlinear mathematical physics.In this report, we study a nonlinear boundary value problem for the inhomogeneous Monge-ampere equation, the right part of which contains power nonlinearities in derivatives and arbitrary nonlinearity from the desired function.Based on linearization, the studied boundary value problems are reduced to a system of ordinary first-order differential equations with initial conditions that depend on the parameter.Methods for constructing exact and approximate solutions of some boundary value problems for the Monge-ampere equation are proposed.Using the Mathcad software package, numerical implementation of methods for constructing approximate solutions of the obtained systems of ordinary differential equations with a parameter is performed.Three-dimensional graphs of exact and approximate solutions of the problems under consideration in the Grafikus service are constructed.

scholarly journals Modified nonlinearities distribution Homotopy Perturbation method as a tool to find power series solutions to ordinary differential equations

Nova Scientia ◽  
2014 ◽  
Vol 6 (12) ◽  
pp. 13 ◽  
Author(s):  
Umberto Filobello-Nino ◽  
Héctor Vázquez-Leal ◽  
Yasir Khan ◽  
D. Pereyra-Díaz ◽  
A. Pérez-Sesma ◽  
...  
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Series Solutions ◽  
Homotopy Perturbation ◽  
Polynomial Coefficients ◽  
Power Series Solutions

In this article, modified non-linearities distribution homotopy perturbation method (MNDHPM) is used in order to find power series solutions to ordinary differential equations with initial conditions, both linear and nonlinear. We will see that the method is particularly relevant in some cases of equations with non-polynomial coefficients and inhomogeneous non-polynomial terms

scholarly journals An exact solution method for Fredholm integro-differential equations

2019 ◽  
pp. 2-8 ◽  
Author(s):  
Kyriaki Tsilika
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Solution Method ◽  
Initial Conditions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Abstract Operator ◽  
Nonlocal Integral Boundary Conditions

Introduction: Linear boundary value problems for Fredholm ordinary integro-differential equations are seldom consideredwith integral boundary conditions in the literature. In our case, integro-differential equations are subject to multipoint or nonlocalintegral boundary conditions. It should be noted that finding exact solutions even for multipoint problems or problems with nonlocalintegral boundary conditions with a differential equation is a difficult task. Purpose: Finding the uniqueness and existencecriterion of solutions for Fredholm ordinary integro-differential equations with multipoint or nonlocal integral boundary conditionsand obtaining exact solutions in closed form of such problems. Results: Within the class of abstract operator equations, for thespecial case of Fredholm integro-differential equations with multipoint or nonlocal integral boundary conditions, a criterion for theexistence and uniqueness of an exact solution is proved and the analytical representation of the solution is given. A direct methodanalytically solving such problems is proposed, in which all calculations are reproducible in any program of symbolic calculations.If the user sets the input parameters and the initial conditions of the problem, the computer codes check the conditions of existenceand uniqueness and of solution generate the analytical solution. The stages of the solution method are illustrated by twoexamples. The article uses computer algebra system Mathematica to demonstrate the results.

Application of New Homotopy Perturbation Method for Solving Partial Differential Equations

2018 ◽  
Vol 15 (2) ◽  
pp. 500-508 ◽  
Author(s):  
Musa R. Gad-Allah ◽  
Tarig M. Elzaki
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Nonlinear Differential Equations ◽  
Novel Technique ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
Linear Differential

In this paper, a novel technique, that is to read, the New Homotopy Perturbation Method (NHPM) is utilized for solving a linear and non-linear differential equations and integral equations. The two most important steps in the application of the new homotopy perturbation method are to invent a suitable homotopy equation and to choose a suitable initial conditions. Comparing between the effects of the method (NHPM), is given exact solution, and the method (HPM), is given approximate solution, in this paper, we make some instances are provided to prove the ability of the method (NHPM). Show that the method (NHPM) is valid and effective, easy and accurate in solving linear and nonlinear differential equations, compared with the Homotopy Perturbation Method (HPM).

scholarly journals The best parameters selection using pso algorithm to solving for ito system by new iterative technique

2020 ◽  
Vol 18 (3) ◽  
pp. 1638
Author(s):  
Karam Adel Abed ◽  
Abeer Abdulkhaleq Ahmad
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Approximate Solutions ◽  
Pso Algorithm ◽  
High Accuracy ◽  
Iterative Technique ◽  
Parameters Selection ◽  
A New Technique ◽  
Best Parameters ◽  
New Iterative Method

<p>The main aim of this study is to obtain the best approximate solution for the nonlinear Ito system by applying the new iterative method, A new technique has been proposed that combines the new iterative method with the particle optimization algorithm. The most important distinctive of this work is the analysis of errors between the exact solution of the system and the approximate solutions, which showed us that these approximate solutions of the proposed technique in particular have high accuracy because they converge significantly from the exact solution.</p>

EXACT SOLUTION OF TASKS OF DYNAMIC MODELING OF PROCESSES IN SYSTEMS OF TRANSPORT LOGISTIC

2019 ◽  
Vol 2 (12) ◽  
pp. 5-13
Author(s):  
O. Ugol’nikov ◽  
B. Demianchuk ◽  
N. Kolesnychenko ◽  
O. Malinovsky
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Decomposition Method ◽  
Dynamic Models ◽  
Initial Conditions ◽  
Operational Calculus ◽  
Approximate Methods ◽  
Coupled Equations ◽  
Linear Algebraic Equations ◽  
Transport Logistics

The dynamic models of processes in transport logistics systems are considered. In the literature, such complex systems as the military transport logistics system or the combat vehicle support system are often modeled as a set of typical system states. These states are interconnected by a large number of transitions of a given intensity, which are carried out with given probabilities. Graphically, this is represented using the so-called graph of states and transitions, and the probabilities of the system being in a particular state are the subject of research in such a graph. The methods available in the literature for studying the dynamic characteristics of state graphs and transitions are analyzed. A description of the changes in probabilities as a function of time is made using systems of differential equations, usually linear. Based on practical requirements, approximate solutions to such systems are usually sought. One of the approximate methods is the decomposition method, in which, instead of a system of coupled equations, a set of independent equations is considered, the solution of which is not difficult. The results of the solution have an accuracy satisfactory from the point of view of practical use. The assumptions based on which the decomposition method can be used are analyzed. It is shown that the accuracy of the obtained results substantially depends on the given initial conditions and should increase over time, when this dependence weakens. A method is proposed for the exact solution of a system of differential equations, free of any assumptions. The use of operational calculus is substantiated, which reduces the solution of a system of linear differential equations to the solution of a system of linear algebraic equations for unknown images of the sought-for Laplace functions. The method is used to describe the process of technical support for the restoration of the transport flow of military logistics. The boundaries of the possibility of applying the results of a simpler approximate solution are established.

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