The Laguerre Collocation Method

Gheorghiu, Călin-Ioan

doi:10.1007/978-3-319-06230-3_4

Cited by 1 publication

(4 citation statements)

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“…Substitution of (26) and (27) into (21) gives the required results (19) and completes the proof of Theorem 3.…”

Section: Modi Ed Generalized Laguerre Coe Cients Of a General-order Dsupporting

confidence: 52%

“…where b q, i are as given in (19). Following the procedure of Doha [38], and after some rather lengthy manipulations, we get,…”

Section: Applications and Numerical Resultsmentioning

confidence: 99%

“…where b q, i are as given in (19). In Table 1, we list the maximum absolute error of Example 2, for di erent values of α, β and N over the interval ( , ).…”

Section: Applications and Numerical Resultsmentioning

confidence: 99%

“…In this work, we attempt to solve di erntial equations using the modi ed generalized Laguerre polynomials jointly with the spectral accurate tau and collocation methods. The Laguerre polynomials and the spectral collocation method for the numerical solution of di erential equations have been extensively used in [19][20][21][22][23][24]. Guo et al [25] applied the mixed generalized Laguerre spectral method for the exterior problems.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the connection coefficients and recurrence relations arising from expansions in series of modified generalized Laguerre polynomials: Applications on a semi-infinite domain

Doha

Youssri

2019

Nonlinear Engineering

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Herein, three important theorems were stated and proved. The first relates the modified generalized Laguerre expansion coefficients of the derivatives of a function in terms of its original expansion coefficients; and an explicit expression for the derivatives of modified generalized Laguerre polynomials of any degree and for any order as a linear combination of modified generalized Laguerre polynomials themselves is also deduced. The second theorem gives new modified generalized Laguerre coefficients of the moments of one single modified generalized Laguerre polynomials of any degree. Finally, the third theorem expresses explicitly the modified generalized Laguerre coefficients of the moments of a general-order derivative of an infinitely differentiable function in terms of its modified generalized Laguerre coefficients. Some spectral applications of these theorems for solving ordinary differential equations with varying coefficients and some specific applied differential problems, by reducing them to recurrence relations in their expansion coefficients of the solution are considered.

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“…Substitution of (26) and (27) into (21) gives the required results (19) and completes the proof of Theorem 3.…”

Section: Modi Ed Generalized Laguerre Coe Cients Of a General-order Dsupporting

confidence: 52%

“…where b q, i are as given in (19). Following the procedure of Doha [38], and after some rather lengthy manipulations, we get,…”

Section: Applications and Numerical Resultsmentioning

confidence: 99%

“…where b q, i are as given in (19). In Table 1, we list the maximum absolute error of Example 2, for di erent values of α, β and N over the interval ( , ).…”

Section: Applications and Numerical Resultsmentioning

confidence: 99%