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

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.

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Solving Some Differential Equations Arising in Electric Engineering Using Hermite Polynomials

Journal of Scientific Research ◽

10.3329/jsr.v12i4.45686 ◽

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.

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A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line

Abstract and Applied Analysis ◽

10.1155/2014/692193 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 4

Author(s):

Ali H. Bhrawy ◽

Abdulrahim AlZahrani ◽

Dumitru Baleanu ◽

Yahia Alhamed

Keyword(s):

Differential Equations ◽

Laguerre Polynomials ◽

Functional Differential Equations ◽

Numerical Results ◽

Half Line ◽

Algebraic Equations ◽

Neutral Functional Differential Equations ◽

Generalized Laguerre Polynomials ◽

Collocation Points ◽

Functional Differential

The modified generalized Laguerre-Gauss collocation (MGLC) method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.

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Laguerre Collocation Method for Solving Fredholm Integro-Differential Equations with Functional Arguments

Journal of Applied Mathematics ◽

10.1155/2014/682398 ◽

2014 ◽

Vol 2014 ◽

pp. 1-12 ◽

Cited By ~ 13

Author(s):

Burcu Gürbüz ◽

Mehmet Sezer ◽

Coşkun Güler

Keyword(s):

Differential Equations ◽

Collocation Method ◽

Matrix Equation ◽

Numerical Experiments ◽

Approximate Solutions ◽

Correction Method ◽

Algebraic Equations ◽

Linear Algebraic Equations ◽

Residual Correction

Laguerre collocation method is applied for solving a class of the Fredholm integro-differential equations with functional arguments. This method transforms the considered problem to a matrix equation which corresponds to a system of linear algebraic equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments. Also, the approximate solutions are corrected by using the residual correction method.

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ON SOLUTIONS OF LINEAR FUNCTIONAL INTEGRAL AND INTEGRO-DIFFERENTIAL EQUATIONS VIA LAGRANGE POLYNOMIALS

Journal of Science and Arts ◽

10.46939/j.sci.arts-21.3-a11 ◽

2021 ◽

Vol 21 (3) ◽

pp. 707-720

Author(s):

ŞUAYİP YÜZBAŞI YÜZBAŞI ◽

MEHMET SEZER

Keyword(s):

Differential Equations ◽

Collocation Method ◽

Linear Functional ◽

Initial Conditions ◽

Functional Integral ◽

Algebraic Equations ◽

Science And Engineering ◽

Lagrange Polynomials ◽

Matrix Operations ◽

Linear Algebraic Equations

In this study, a matrix-collocation method is developed numerically to solve the linear Fredholm-Volterra-type functional integral and integro-differential equations. The linear functional integro-differential equations are considered under initial conditions. The mentioned type problems often appear in various branches of science and engineering such as physics, biology, mechanics, electronics. The method essentially is a collocation method based on the Lagrange polynomials and matrix operations. By using presented method, the problem is reduced to a system of linear algebraic equations. The solution of this system gives the coefficients of assumed solution. An error analysis based on the residual function is studied. Some examples are solved to demonstrate the accuracy and efficiency of the method.

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The weighted Cauchy problem for linear functional differential equations with strong singularities

Georgian Mathematical Journal ◽

10.1515/gmj.2011.0034 ◽

2011 ◽

Vol 18 (3) ◽

pp. 577-586

Author(s):

Zaza Sokhadze

Keyword(s):

Cauchy Problem ◽

Differential Equations ◽

Linear Functional ◽

Functional Differential Equations ◽

Sufficient Conditions ◽

Initial Point ◽

Higher Order ◽

Well Posedness ◽

Deviating Arguments ◽

Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

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