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.   

scholarly journals Generalized Spline Approach For Solving System of Linear Fractional Volterra Integro-Differential Equations

2018 ◽  
Vol 31 (1) ◽  
pp. 222
Author(s):  
Nabaa Najdi Hasan ◽  
Doaa Ahmed Hussien
Keyword(s):  
Differential Equation ◽  
Linear System ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Suggested Method ◽  
Spline Method ◽  
Algebraic Equations ◽  
Integro Differential Equation ◽  
Linear Algebraic Equations

    In this paper generalized spline method is used for solving linear system of fractional integro-differential equation approximately. The suggested method reduces the system to system of  linear algebraic equations. Different orders of fractional derivative for test example is given in this paper to show the accuracy and applicability of the presented method.

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.

Solving Nonlinear Volterra | Fredholm Integro-differential Equations Using the Modified Adomian Decomposition Method

2009 ◽  
Vol 9 (4) ◽  
pp. 321-331 ◽  
Author(s):  
M. A. Fariborzi Araghi ◽  
Sh. Sadigh Behzadi
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Error Bound ◽  
Decomposition Method ◽  
Numerical Scheme ◽  
Adomian Decomposition Method ◽  
Integro Differential Equation ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

AbstractIn this paper, a nonlinear Volterra | Fredholm integro-differential equation is solved by using the modified Adomian decomposition method (MADM). The approximate solution of this equation is calculated in the form of a series in which its components are computed easily. The accuracy of the proposed numerical scheme is examined by comparison with other analytical and numerical results. The existence, uniqueness and convergence and an error bound of the proposed method are proved. Some examples are presented to illustrate the efficiency and the performance of the modified decomposition method.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

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.

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 Existence and uniqueness theorem for a solution of fuzzy differential equations

1999 ◽  
Vol 22 (2) ◽  
pp. 271-279 ◽  
Author(s):  
Jong Yeoul Park ◽  
Hyo Keun Han
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Fuzzy Differential Equation ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of A Solution

By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equationx′(t)=f(t,x(t)),x(t0)=x0. We also consider anϵ-approximate solution of the above fuzzy differential equation.

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