Polynomial solution of the single degree of freedom system by Taylor matrix method

Kurt, Nurcan; Çevik, Mehmet

doi:10.1016/j.mechrescom.2008.05.001

Cited by 20 publications

(16 citation statements)

References 11 publications

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“…where (4), we replace the last m rows of the matrix (27) by the m-row matrix (28), and construct the new augmented matrix [15,16].…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…This is an important branch of modern mathematics and arise frequently in many applied areas which include engineering, mechanics, physics, chemistry, astronomy, biology, economics, potential theory, electrostatics, etc. [15][16][17]. Many problems of physics and engineering lead naturally to the resolution of differential and integral equations in bounded or unbounded domains.…”

Section: Introductionmentioning

confidence: 99%

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Laguerre polynomial solution of high- order linear Fredholm integro-differential equations

Sezer¹,

Savaşaneril²

2016

ntmsci

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In this paper, a Laguerre matrix method is developed to find an approximate solution of linear differential, integral and integro-differential equations with variable coefficients under mixed conditions in terms of Laguerre polynomials. For this purpose, Laguerre polynomials are used in the interval [0,b]. The proposed method converts these equations into matrix equations, which correspond to systems of linear algebraic equations with unknown Laguerre coefficients. The solution function is obtained easily by solving these matrix equations. The examples of these kinds of equations are solved by using this new method and the results are discussed and it is seen that the present method is accurate, efficient and applicable.

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“…where (4), we replace the last m rows of the matrix (27) by the m-row matrix (28), and construct the new augmented matrix [15,16].…”

Section: Methods Of Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Laguerre polynomial solution of high- order linear Fredholm integro-differential equations

Sezer¹,

Savaşaneril²

2016

ntmsci

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“…If max 10 −k q = 10 −k (k positive integer) is prescribed, then the truncation limit N is increased until the difference E i,N (t q ) at each of the points becomes smaller than the prescribed 10 −k , see [2,14,24].…”

Section: Accuracy Of the Solutionsmentioning

confidence: 99%

Bessel collocation approach for approximate solutions of Hantavirus infection model

Yüzbaşı¹

2017

ntmsci

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Abstract:In this study, a collocation method is introduced to find the approximate solutions of Hantavirus infection model which is a system of nonlinear ordinary differential equations. The method is based on the Bessel functions of the first kind, matrix operations and collocation points. This method converts Hantavirus infection model into a matrix equation in terms of the Bessel functions of first kind, matrix operations and collocation points. The matrix equation corresponds to a system of nonlinear equations with the unknown Bessel coefficients. The reliability and efficiency of the suggested scheme are demonstrated by numerical applications and all numerical calculations have been done by using a program written in Maple.

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“…There are many branches of science, such as control theory and financial mathematics, which leads to integro-differential equations (IDEs). In modern mathematics, IDEs mostly occur in many applied areas including engineering, physics and biology [1][2][3][4][5][6]. The resolution of many problems in physics and engineering leads to differential and integral equations in bounded or unbounded domains.…”

Section: Introductionmentioning

confidence: 99%

Laguerre approach for solving system of linear Fredholm integro-differential equations

2018

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A numerical scheme has been developed for solving the system of linear Fredholm integro-differential equations subject to the mixed conditions using Laguerre polynomials. Using collocation method, the system of Fredholm integro-differential equations has been transformed to the system of linear equations in unknown Laguerre coefficients, which leads to the solution in terms of Laguerre polynomials. Moreover, the accuracy and applicability of the scheme have been compared with Tau method and Adomian decomposition method that reveals the proposed scheme to be more efficient.

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Polynomial solution of the single degree of freedom system by Taylor matrix method

Cited by 20 publications

References 11 publications

Laguerre polynomial solution of high- order linear Fredholm integro-differential equations

Laguerre polynomial solution of high- order linear Fredholm integro-differential equations

Bessel collocation approach for approximate solutions of Hantavirus infection model

Laguerre approach for solving system of linear Fredholm integro-differential equations

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