First Leaves: A Tutorial Introduction to Maple V

Char, Bruce W.; Geddes, K. O.; Gonnet, Gastón H.; Leong, Benton; Monagan, Michael; Watt, Stephen M.

doi:10.1007/978-1-4615-6996-1

Cited by 132 publications

(64 citation statements)

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“…(26) valid for all n, e.g. with the help of Maple [12], being an easy-to-use computer algebra program. Hence, in the contrast to a pure numerical scheme (say, in a fashion of Beausoleil [7]), one obtains analytical, rather than numerical, result which is already well adapted for further numerical calculation (onefold integration).…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Light-shift calculation in the ns-states of hydrogenic systems

Yakhontov

Jungmann

1996

Z Phys D - Atoms, Molecules and Clusters

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Section: Resultsmentioning

confidence: 99%

“…Here the integral is taken along some contour γ in the complex plane of t. It has to be chosen to comply both with (12) and the form of the contour γ 1 (see below) in the integral representation of the right-hand side of (11). Besides, after passing along γ the integrand of (15) should return back to its initial value.…”

Section: General Considerationmentioning

confidence: 99%

Light-shift calculation in the ns-states of hydrogenic systems

Yakhontov

Jungmann

1996

Z Phys D - Atoms, Molecules and Clusters

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“…The exact value of the above integral can be computed by using the Fubini Type formula given in eqn (19 ) ,instead of this we show here the direct application of Theorem 2 given in this paper to obtain the exact value of the integral over the pentagon of The above equn (26) suggests that one can straight way proceed to the application Gauss Legendre quadrature which will not put any conditions on p,q. Thus numerical integration is simple and efficient.…”

Section: Page 14758mentioning

confidence: 91%

“…Thus numerical integration is simple and efficient. But we have to impose several conditions on p,q to obtain the exact integration formulas for the evaluation of the above integral expression in eqn (19) and eqn (24).The explicit formulas are now listed below.…”

Section: Page 14758mentioning

confidence: 99%

A New Approach to Automatic Generation of An All Pentagonal Finite Element Mesh For Numerical Computations Over Convex Polygonal Domains

Rathod¹,

Devi²

2016

IJECS

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A new method is presented for subdividing a large class of solid objects into topologically simple subregions suitable for automatic finite element meshing with pentagonal elements. It is known that one can improve the accuracy of the finite element solution by uniformly refining a triangulation or uniformly refining a quadrangulation. Recently a refinement scheme of pentagonal partition was introduced in [31,32,33]. It is demonstrated that the numerical solution based on the pentagonal refinement scheme outperforms the solutions based on the traditional triangulation refinement scheme as well as quadrangulation refinement scheme. It is natural to ask if one can create a hexagonal refinement or general polygonal refinement schemes with a hope to offer even further improvement. It is shown in literature that one cannot refine a hexagon using hexagons of smaller size. In general, one can only refine an n-gon by n-gons of smaller size if n ≤ 5. Furthermore, we introduce a refinement scheme of a general polygon based on the pentagon scheme. This paper first presents a pentagonalization (or pentagonal conversion) scheme that can create a pentagonal mesh from any arbitrary mesh structure. We also introduce a pentagonal preservation scheme that can create a pentagonal mesh from any pentagonal mesh. This paper then presents a new numerical integration technique proposed earlier by the first author and co-workers, known as boundary integration method [34][35][36][37][38][39][40] is now applied to arbitrary polygonal domains using pentagonal finite element mesh. Numerical results presented for a few benchmark problems in the context of pentagonal domains with composite numerical integration scheme over triangular finite elements show that the proposed method yields accurate results even for low order Gauss Legendre Quadrature rules. Our numerical results suggest that the refinement scheme for pentagons and polygons may lead to higher accuracy than the uniform refinement of triangulations and quadrangulations.

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“…With the assistance of the MAPLE language [13] etc. These results inspire the general ansatz This did not disprove the obtrusive hypothesis that D L are polynomials in a with integer coefficients and with a growing degree L = L(K) = (K + 1)(K + 2)/2 − 3.…”

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confidence: 99%

Perturbed Pöschl–Teller oscillators

Znojil

2000

Physics Letters A

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First Leaves: A Tutorial Introduction to Maple V

Cited by 132 publications

References 0 publications

Light-shift calculation in the ns-states of hydrogenic systems

Light-shift calculation in the ns-states of hydrogenic systems

A New Approach to Automatic Generation of An All Pentagonal Finite Element Mesh For Numerical Computations Over Convex Polygonal Domains

Perturbed Pöschl–Teller oscillators

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