scholarly journals Bernstein Collocation Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations in the Most General Form

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ayşegül Akyüz-Daşcıoğlu ◽  
Neşe İşler Acar ◽  
Coşkun Güler
Keyword(s):  
Collocation Method ◽  
Integrodifferential Equation ◽  
Bernstein Polynomials ◽  
Approximate Solutions ◽  
Integrodifferential Equations ◽  
Numerical Examples ◽  
Collocation Points ◽  
Volterra Integrodifferential Equation ◽  
Quasilinearization Technique

A collocation method based on the Bernstein polynomials defined on the interval[a,b]is developed for approximate solutions of the Fredholm-Volterra integrodifferential equation (FVIDE) in the most general form. This method is reduced to linear FVIDE via the collocation points and quasilinearization technique. Some numerical examples are also given to demonstrate the applicability, accuracy, and efficiency of the proposed method.

scholarly journals Solving Some Differential Equations Arising in Electric Engineering Using Hermite Polynomials

2020 ◽  
Vol 12 (4) ◽  
pp. 517-523
Author(s):  
G. Singh ◽  
I. Singh
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Collocation Method ◽  
Hermite Polynomials ◽  
Electric Circuit ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Electric Engineering ◽  
Collocation Points ◽  
Linear Algebraic Equations

In this paper, a collocation method based on Hermite polynomials is presented for the numerical solution of the electric circuit equations arising in many branches of sciences and engineering. By using collocation points and Hermite polynomials, electric circuit equations are transformed into a system of linear algebraic equations with unknown Hermite coefficients. These unknown Hermite coefficients have been computed by solving such algebraic equations. To illustrate the accuracy of the proposed method some numerical examples are presented.

scholarly journals Solving Fuzzy Volterra Integrodifferential Equations of Fractional Order by Bernoulli Wavelet Method

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
R. Mastani Shabestari ◽  
R. Ezzati ◽  
T. Allahviranloo
Keyword(s):  
Integrodifferential Equation ◽  
Matrix Equation ◽  
Matrix Method ◽  
Integrodifferential Equations ◽  
Algebraic Equations ◽  
Wavelet Method ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Bernoulli Wavelet ◽  
Fractional Integrodifferential Equation

A matrix method called the Bernoulli wavelet method is presented for numerically solving the fuzzy fractional integrodifferential equations. Using the collocation points, this method transforms the fuzzy fractional integrodifferential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown coefficients. To illustrate the method, it is applied to certain fuzzy fractional integrodifferential equations, and the results are compared.

scholarly journals Bessel Collocation Method for Solving Fredholm–Volterra Integro-Fractional Differential Equations of Multi-High Order in the Caputo Sense

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2354
Author(s):  
Shazad Shawki Ahmed ◽  
Shabaz Jalil MohammedFaeq
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Linear Algebraic Equation ◽  
Approximate Solutions ◽  
New Approach ◽  
Numerical Examples ◽  
Time Symmetry ◽  
Collocation Points ◽  
The Matrix ◽  
Fractional Differential

The approximate solutions of Fredholm–Volterra integro-differential equations of multi-fractional order within the Caputo sense (F-VIFDEs) under mixed conditions are presented in this article apply a collocation points technique based completely on Bessel polynomials of the first kind. This new approach depends particularly on transforming the linear equation and conditions into the matrix relations (some time symmetry matrix), which results in resolving a linear algebraic equation with unknown generalized Bessel coefficients. Numerical examples are given to show the technique’s validity and application, and comparisons are made with existing results by applying this process in order to express these solutions, most general programs are written in Python V.3.8.8 (2021).

scholarly journals Numerical Solution of Nonlinear Fredholm Integrodifferential Equations by Hybrid of Block-Pulse Functions and Normalized Bernstein Polynomials

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
S. H. Behiry
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Present Method ◽  
Bernstein Polynomials ◽  
Integrodifferential Equations ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Nonlinear Algebraic Equations

A numerical method for solving nonlinear Fredholm integrodifferential equations is proposed. The method is based on hybrid functions approximate. The properties of hybrid of block pulse functions and orthonormal Bernstein polynomials are presented and utilized to reduce the problem to the solution of nonlinear algebraic equations. Numerical examples are introduced to illustrate the effectiveness and simplicity of the present method.

scholarly journals A numerical method for solving systems of higher order linear functional differential equations

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 15-25 ◽  
Author(s):  
Suayip Yüzbasi ◽  
Emrah Gök ◽  
Mehmet Sezer
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Legendre Polynomials ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Approximate Solutions ◽  
Algebraic Equations ◽  
Collocation Points ◽  
Linear Algebraic Equations ◽  
Functional Differential

AbstractFunctional differential equations have importance in many areas of science such as mathematical physics. These systems are difficult to solve analytically.In this paper we consider the systems of linear functional differential equations [1-9] including the term y(αx + β) and advance-delay in derivatives of y .To obtain the approximate solutions of those systems, we present a matrix-collocation method by using Müntz-Legendre polynomials and the collocation points. For this purpose, to obtain the approximate solutions of those systems, we present a matrix-collocation method by using Müntz-Legendre polynomials and the collocation points. This method transform the problem into a system of linear algebraic equations. The solutions of last system determine unknown co-efficients of original problem. Also, an error estimation technique is presented and the approximate solutions are improved by using it. The program of method is written in Matlab and the approximate solutions can be obtained easily. Also some examples are given to illustrate the validity of the method.

scholarly journals ON FRACTIONAL VOLTERRA INTEGRODIFFERENTIAL EQUATIONS WITH FRACTIONAL INTEGRABLE IMPULSES

2019 ◽  
Vol 24 (3) ◽  
pp. 457-477 ◽  
Author(s):  
Sagar T. Sutar ◽  
Kishor D. Kucche Kucche
Keyword(s):  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Integrodifferential Equations ◽  
Compact Interval ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Volterra Integrodifferential Equation

We consider a class of nonlinear fractional Volterra integrodifferential equation with fractional integrable impulses and investigate the existence and uniqueness results in the Bielecki’s normed Banach spaces. Further, Bielecki-Ulam type stabilities have been demonstrated on a compact interval. A concrete example is provided to illustrate the outcomes we acquired.

scholarly journals Polynomial spline collocation methods for second-order Volterra integrodifferential equations

2004 ◽  
Vol 2004 (56) ◽  
pp. 3011-3022 ◽  
Author(s):  
Edris Rawashdeh ◽  
David Mcdowell ◽  
Leela Rakesh
Keyword(s):  
Integrodifferential Equation ◽  
Polynomial Spline ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Collocation Methods ◽  
Spline Collocation ◽  
Initial Value ◽  
Volterra Integrodifferential Equation

We have presented a method for the construction of an approximation to the initial-value second-order Volterra integrodifferential equation (VIDE). The polynomial spline collocation methods described here give a superconvergence to the solution of the equation.

scholarly journals An Approximation Method for Solving Volterra Integrodifferential Equations with a Weighted Integral Condition

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
A. Guezane-Lakoud ◽  
N. Bendjazia ◽  
R. Khaldi
Keyword(s):  
Hilbert Space ◽  
Analytical Solution ◽  
Approximation Method ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Integral Condition ◽  
Approximate Solutions ◽  
Integrodifferential Equations ◽  
Numerical Examples ◽  
Weighted Integral

We apply the reproducing kernel Hilbert space (RKHS) method for getting analytical and approximate solutions for second-order hyperbolic integrodifferential equations with a weighted integral condition. The analytical solution is represented in the form of series; thus, then-terms approximate solutions are obtained. The results of the numerical examples are compared with the exact solutions to illustrate the accuracy and the effectivity of this method.

scholarly journals BOOLE COLLOCATION METHOD BASED ON RESIDUAL CORRECTION FOR SOLVING LINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATION

2020 ◽  
Vol 20 (3) ◽  
pp. 597-610
Author(s):  
HALE GUL DAG ◽  
KUBRA ERDEM BICER
Keyword(s):  
Differential Equation ◽  
Error Analysis ◽  
Matrix Equation ◽  
Approximate Solutions ◽  
Residual Function ◽  
Numerical Examples ◽  
Integro Differential Equation ◽  
Collocation Points ◽  
Residual Correction ◽  
The Given

In this study, a Boole polynomial based method is presented for solving the linear Fredholm integro-differential equation approximately. In this method, the given problem is reduced to a matrix equation. The solution of the obtained matrix equation is found by using Boole polynomial, its derivatives and collocation points. This solution is obtained as the truncated Boole series which are defined in the interval [a,b]. In order to demonstrate the validity and applicability of the method, numerical examples are included. Also, the error analysis related with residual function is performed and the found approximate solutions are calculated.

scholarly journals Existence, Uniqueness, and Characterization Theorems for Nonlinear Fuzzy Integrodifferential Equations of Volterra Type

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Omar Abu Arqub ◽  
Shaher Momani ◽  
Saleh Al-Mezel ◽  
Marwan Kutbi
Keyword(s):  
Approximate Solutions ◽  
Integrodifferential Equations ◽  
Banach Fixed Point Theorem ◽  
Constraint Condition ◽  
Volterra Type ◽  
Generalized Differentiability ◽  
Volterra Integrodifferential Equation ◽  
Strongly Generalized Differentiability ◽  
Characterization Theorems ◽  
Main Ideas

Existence and uniqueness theorem are the tool which makes it possible for us to conclude that there exists only one solution to a given problem which satisfies a constraint condition. How does it work? Why is it the case? We believe it, but it would be interesting to see the main ideas behind this. To this end, in this paper, we investigate existence, uniqueness, and other properties of solutions of a certain nonlinear fuzzy Volterra integrodifferential equation under strongly generalized differentiability. The main tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain integral inequality with explicit estimate. Also, some results for characterizing solution by an equivalent system of crisp Volterra integrodifferential equations are presented. In this way, a new direction for the methods of analytic and approximate solutions is proposed.

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