�ber lineare Differenzengleichungen und eine Anwendung auf lineare Differentialgleichungen mit Polynomkoeffizienten

Summary. Stability analysis of reducible quadrature methods for Volterra integral equations based on the test equationis presented. The concept of absolute stability is defined and necessary and sufficient conditions for the method to be absolutely stable for given 2, #, and v are derived. These conditions are illustrated for the class of 0-methods for integral equations. The main tool in our stability analysis is the theory of difference equations of Poincar6 type.

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“…It follows from the theorem of Perron [16] (see also [17], Satz A) that there exists a solution y. of (19) such that…”

Section: J=2kmentioning

confidence: 95%

Stability of reducible quadrature methods for Volterra integral equations of the second kind

Bakke

Jackiewicz

1985

Numer. Math.

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“…The set of coefficients {a k,σ } and {b j } are solutions of the difference equations ( 6) and (10), respectively. According to the Perron-Kreuser theorem on difference equations [15,21,22],…”

Section: The Eigenvaluesmentioning

confidence: 99%

A naive procedure for computing angular spheroidal functions

Sesma¹

2016

Preprint

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An algorithm for computing eigenvalues and eigenfunctions of the angular spheroidal wave equation, based on a known but scarcely used method, is developed. By requiring the regularity of the wave function, represented by its series expansion, the eigenvalues appear as the zeros of a one variable function easily computable. The iterative extended Newton method is suggested as especially suitable for determining those zeros. The computation of the eigenfunctions is then immediate. The usefulness of the method, applicable also in the case of complex values of the "prolateness" parameter, is illustrated by comparing its results with those of procedures used by other authors.

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“…The coefficients must obey the recurrence relations (12) and (13) that are but third order difference equations. The Perron-Kreuser theorem (Perron, 1959) predicts for each one of them a unique (save for multiplication by a constant) dominant solution that can be obtained starting, for instance, with a 0,k = 1, b 0,l = 1, k = 3, 4, l = 5, 6,…”

Section: Formal Solutionsmentioning

confidence: 99%

An algorithm to obtain global solutions of the double confluent Heun equation

2008

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Abstract. A procedure is proposed to construct solutions of the double confluent Heun equation with a determinate behaviour at the singular points. The connection factors are expressed as quotients of Wronskians of the involved solutions. Asymptotic expansions are used in the computation of those Wronskians. The feasibility of the method is shown in an example, namely, the Schrödinger equation with a quasi-exactly-solvable potential

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�ber lineare Differenzengleichungen und eine Anwendung auf lineare Differentialgleichungen mit Polynomkoeffizienten

Cited by 18 publications

References 8 publications

Stability of reducible quadrature methods for Volterra integral equations of the second kind

Stability of reducible quadrature methods for Volterra integral equations of the second kind

A naive procedure for computing angular spheroidal functions

An algorithm to obtain global solutions of the double confluent Heun equation

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