Reliable Computation of the Zeros of Solutions of Second Order Linear ODEs Using a Fourth Order Method

DOI10.1137/090747762zbMath1211.65056OpenAlexW2075671192MaRDI QIDQ3084196

Javier Segura

Publication date: 15 March 2011

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10902/3207

zbMATH Keywords

algorithmnumerical resultsfixed point methodconfluent hypergeometric functionsGauss hypergeometric functionszeros of solutionsSturm theoremsecond order ODEs

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Numerical computation of solutions to single equations (65H05) Linear ordinary differential equations and systems (34A30) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Numerical approximation and evaluation of special functions (33F05)

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Computing the complex zeros of special functions ⋮ On the complex zeros of Airy and Bessel functions and those of their derivatives ⋮ The Schwarzian-Newton method for solving nonlinear equations, with applications ⋮ A third-order iterative algorithm for inversion of cumulative central beta distribution ⋮ On the Numerical Calculation of the Roots of Special Functions Satisfying Second Order Ordinary Differential Equations ⋮ Noniterative Computation of Gauss--Jacobi Quadrature ⋮ Asymptotic expansions of Jacobi polynomials and of the nodes and weights of Gauss-Jacobi quadrature for large degree and parameters in terms of elementary functions ⋮ Computing the real zeros of cylinder functions and the roots of the equation \(x{\mathcal C}_{\nu}'(x)+\gamma{\mathcal C}_{\nu}(x)=0\). ⋮ Fast and reliable high-accuracy computation of Gauss-Jacobi quadrature ⋮ Fast, reliable and unrestricted iterative computation of Gauss-Hermite and Gauss-Laguerre quadratures

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