Laguerre polynomial approach for solving linear delay difference equations

Gülsu, Mustafa; Gürbüz, Burcu; Öztürk, Yalçın; Sezer, Mehmet

doi:10.1016/j.amc.2011.01.112

Cited by 47 publications

(31 citation statements)

References 21 publications

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“…Here, the standard Laguerre polynomials and their Rodriguez Formula , respectively, are defined by

L_{n} (t) MathClass-rel= {falsefalse}_{MathClass-op\sum}^{r MathClass-rel= 0} \frac{{(MathClass-bin- 1)}^{r}}{r MathClass-punc!} ((), \begin{matrix} falsenonefalsearray \\ arraycenter n \\ arraycenter r \end{matrix}) t^{r} MathClass-punc, 0 MathClass-rel\leq a MathClass-rel\leq t MathClass-rel\leq b MathClass-rel< MathClass-rel\infty

and

L_{0} (t) MathClass-rel= 1 MathClass-punc, L_{n} (t) MathClass-rel= \frac{e^{t}}{n MathClass-punc!} \frac{d^{n}}{d t^{n}} ((), t^{n} e^{MathClass-bin- t}) MathClass-punc, (n MathClass-rel= 1 MathClass-punc, 2 MathClass-punc, MathClass-op\dots) MathClass-punc.

…”

Section: Description Of the Problemmentioning

confidence: 99%

“…On the other hand, the Laguerre polynomials satisfy the recurrence relation

L_{n}^{(1)} (t) MathClass-rel= L_{n MathClass-bin- 1}^{(1)} (t) MathClass-bin- L_{n MathClass-bin- 1} (t) MathClass-punc, L_{0}^{(1)} (t) MathClass-rel= 0 MathClass-punc.

…”

Section: Description Of the Problemmentioning

confidence: 99%

“…Here, the standard Laguerre polynomials and their Rodriguez Formula [1,2], respectively, are defined by…”

Section: Description Of the Problemmentioning

confidence: 99%

“…Recently, the residual error estimation has been used for residual correction [29,30], the error estimation of the Tau method for integro-differential equations [31] and the error estimation of the Bessel collocation method for the multi-pantograph equations [32]. Now, we modify the error estimation studied in [29][30][31][32] for the Laguerre series solutions of the problem (1)- (2).…”

Section: Error Analysis Based On Residual Functionmentioning

confidence: 99%

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Laguerre matrix method with the residual error estimation for solutions of a class of delay differential equations

Yüzbaşı

Gök

Sezer

2013

Math. Meth. Appl. Sci.

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In this study, a practical matrix method based on Laguerre polynomials is presented to solve the higher‐order linear delay differential equations with constant coefficients and functional delays under the mixed conditions. Also, an error analysis technique based on residual function is developed and applied to some problems to demonstrate the validity and applicability of the method. In addition, an algorithm written in Matlab is given for the method. Copyright © 2013 John Wiley & Sons, Ltd.

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“…Here, the standard Laguerre polynomials and their Rodriguez Formula , respectively, are defined by

L_{n} (t) MathClass-rel= {falsefalse}_{MathClass-op\sum}^{r MathClass-rel= 0} \frac{{(MathClass-bin- 1)}^{r}}{r MathClass-punc!} ((), \begin{matrix} falsenonefalsearray \\ arraycenter n \\ arraycenter r \end{matrix}) t^{r} MathClass-punc, 0 MathClass-rel\leq a MathClass-rel\leq t MathClass-rel\leq b MathClass-rel< MathClass-rel\infty

and

L_{0} (t) MathClass-rel= 1 MathClass-punc, L_{n} (t) MathClass-rel= \frac{e^{t}}{n MathClass-punc!} \frac{d^{n}}{d t^{n}} ((), t^{n} e^{MathClass-bin- t}) MathClass-punc, (n MathClass-rel= 1 MathClass-punc, 2 MathClass-punc, MathClass-op\dots) MathClass-punc.

…”

Section: Description Of the Problemmentioning

confidence: 99%

“…On the other hand, the Laguerre polynomials satisfy the recurrence relation

L_{n}^{(1)} (t) MathClass-rel= L_{n MathClass-bin- 1}^{(1)} (t) MathClass-bin- L_{n MathClass-bin- 1} (t) MathClass-punc, L_{0}^{(1)} (t) MathClass-rel= 0 MathClass-punc.

…”

Section: Description Of the Problemmentioning

confidence: 99%

“…Here, the standard Laguerre polynomials and their Rodriguez Formula [1,2], respectively, are defined by…”

Section: Description Of the Problemmentioning

confidence: 99%

Section: Error Analysis Based On Residual Functionmentioning

confidence: 99%

See 2 more Smart Citations

Laguerre matrix method with the residual error estimation for solutions of a class of delay differential equations

Yüzbaşı

Gök

Sezer

2013

Math. Meth. Appl. Sci.

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“…The Generalized Laguerre polynomial is widely used in numerical analysis [1,2,3] and Quantum [4]. It is defined with three-term recurrence relation as follow.…”

Section: Introductionmentioning

confidence: 99%

Accurate Evaluation of Finite Laguerre Series

2017

The 5th International Conference on Advanced Computer Science Applications and Technologies (ACSAT 2017)

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Abstract.A compensated algorithm is presented to evaluate finite Laguerre series. We record round-off error in Clenshaw algorithm by using error-free transformations (EFTs). In this work, we establish a valid error estimate that is as accurate as the Clenshaw scheme using twice the working precision. Numerical experiments illustrate that our compensated algorithm is more accurate than the Clenshaw algorithm and faster than the DDClenshaw algorithm (Clenshaw in double-double arithmetic).

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Numerical solution for high‐order linear complex differential equations with variable coefficients

Düşünceli

Çelık

2017

Numerical Methods Partial

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In this paper, we have obtained the numerical solutions of complex differential equations with variable coefficients by using the Legendre Polynomials and we have performed it on two test problems. Then, we applied with different technical of error analysis to the test problems. When we compared exact solutions and numerical solutions of tables and graphs, we realized that our method is reliable, practical, and functional.

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Laguerre polynomial approach for solving linear delay difference equations

Cited by 47 publications

References 21 publications

Laguerre matrix method with the residual error estimation for solutions of a class of delay differential equations

Laguerre matrix method with the residual error estimation for solutions of a class of delay differential equations

Accurate Evaluation of Finite Laguerre Series

Numerical solution for high‐order linear complex differential equations with variable coefficients

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