Evaluation of prolate spheroidal function by solving the corresponding differential equations

Абрамов, А. А.; Dyshko, A. L.; Konyukhova, N. B.; Pak, T. V.; Pariiskii, B.S.

doi:10.1016/0041-5553(84)90110-1

Cited by 19 publications

(9 citation statements)

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“…This technique exploits a generalized Priifer transformation, which has also been successfully used for solving various similar problems (see [7,81). The merit of the above technique can be illustrated from [9], where the solution of an acoustic wave-scattering problem by a general ellipsoid has been expanded in terms of the Lamb wave functions and multiple results of the calculations have been plotted.…”

Section: Resultsmentioning

confidence: 99%

Partial waves in the nonspherical case

Levitina¹,

Brändas²

1996

Int. J. Quantum Chem.

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mMany quantum mechanical problems are separable in one or several of the standard classifications of general coordinate systems. The associated solution is most conveniently evaluated using expansions in Lam6 wave functions. We give here some preliminary numerical results displaying the continuous distortion of an s-, p-, and d-wave spherical harmonic. The results indicate rather surprising features which may be useful in general quantum mechanical contexts. 0 1996 John Wiley & Sons, Inc.

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Section: Resultsmentioning

confidence: 99%

Partial waves in the nonspherical case

Levitina¹,

Brändas²

1996

Int. J. Quantum Chem.

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“…The numerical method presented above was successfully applied to various problems in oceanology [5], nuclear physics [6][7][8], radiophysics [9,10], and acoustics [3]. 5.2.…”

Section: Resultsmentioning

confidence: 99%

Transfer of admissible boundary conditions from a singular point for systems of linear ordinary differential equations

Абрамов¹,

Konyukhova²

1986

Russian Journal of Numerical Analysis and Mathematical Modelling

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A review is given of the results obtained by the authors on the topic formulated in the title. New results are also presented: methods more general than those suggested earlier are described for constructing admissible boundary conditions at a singular point in the case of systems of first-order equations, and generalized systems of second-order equations with pole-type singularities are analysed, special attention being focused on the conditions of boundedness of the solutions at a singular point and to the emission-type conditions at infinity.The paper gives a definition of the admissible boundary condition at a pole of a system of linear ordinary differential equations. A sufficiently wide class of linear relations is specified, which can provide admissible boundary conditions at a singular point. A particular case covered by this class is the practically important case of emission-type boundary conditions at infinity for systems of second-order equations. Methods of transfer of admissible boundary conditions from singularities in solving singular boundary value problems are described. The results on the application of the suggested methods to solving specific applied problems encountered in oceanology, nuclear physics, radiophysics and acoustics are presented.The present paper is closely related to earlier papers [1,2,11] which are not cited in the text. The results to be described below were briefly outlined earlier in [4]. DEFINITION OF ADMISSIBLE BOUNDARY CONDITIONSConsider on the interval [Ο,α] a system of η homogeneous linear ordinary differential equationswhere r is a positive integer. Assume that the matrix A(t) is continuous on the interval [Ο, a], and can be approximated, at small i, by the convergent (or asymptotic) seriesThe point 0 is a singular point of system (1.1). Let us consider the solutions of (1.1) on a half-open interval [Ο,α]. We introduce the concept of admissible boundary condition at a singular point forOriginally published in Russian as the preprint "Transfer of admissible boundary conditions from a singular point for systems of linear ordinary differential equations", Vychislit. Tsentr Akad. Nauk SSSR, Moscow, 1985. Brought to you by | University of Glasgow Library Authenticated Download Date | 6/25/15 7:11 AM

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“…Results of numerical experiments showing that SWFs can be used in principle for obtaining flaw images with superresolution are presented in [18]. Unfortunately, calculation of high-order SWFs, which are required for practical applications, is very complicated; e.g., in [19] this process involved numerical solution of the corresponding differential equation.…”

Section: Limiting Longitudinal Resolutionmentioning

confidence: 99%

Application of Superresolution Methods for Expert Control of Cylindrical Objects

Базулин

2005

Russ J Nondestruct Test

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The possibility of the combined application of the extrapolation procedure to the spectrum of echo signals during construction of its AR model and of the algorithm for the production of flaw images using a multibeam method of projection in the spectral space (PSS) for testing cylindrical objects is shown. Improvement of the quality of flaw images due to a significant decrease in the "side lobe" levels in the point-spread function is demonstrated in a model experiment. These methods may prove to be especially efficient for testing metallurgical flaws in wheel pairs of rolling stock, workpieces for turbine rotors, and similar items.

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Evaluation of prolate spheroidal function by solving the corresponding differential equations

Cited by 19 publications

References 1 publication

Partial waves in the nonspherical case

Partial waves in the nonspherical case

Transfer of admissible boundary conditions from a singular point for systems of linear ordinary differential equations

Application of Superresolution Methods for Expert Control of Cylindrical Objects

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