Search results for "Singular differential equations"

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Multidomain spectral method for the Gauss hypergeometric function

2018

International audience; We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius’ method and Moebius transformations in the vicinity of each of the singular points of the hypergeometric equation, which leads to a natural decomposition of the real axis into domains. In each domain, solutions to the hypergeometric equation are constructed via the well-conditioned ultraspherical spectral method. The solutions are matched at the domain boundaries to lead to a solution which is analytic on the whole compactified real line R∪∞, except for the singular points and cuts of the Rie…

Singular differential equationsMathematics::Classical Analysis and ODEsRiemann sphere[MATH] Mathematics [math]010103 numerical & computational mathematics01 natural sciencessymbols.namesakeFOS: MathematicsHypergeometric functionMathematics - Numerical Analysis[MATH]Mathematics [math]0101 mathematicsHypergeometric functionQAMathematicsLaplace's equationApplied MathematicsRiemann surfaceMathematical analysisNumerical Analysis (math.NA)[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]Hypergeometric distribution010101 applied mathematicsSpectral methodsHarmonic functionOrdinary differential equationsymbolsSpectral method[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]Numerical Algorithms
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