A Numerical Method for Evaluating Zeros of Solutions of Second-Order Linear Differential Equations

DOI10.2307/2008435zbMath0676.65041OpenAlexW4245467701MaRDI QIDQ3831935

Renato Spigler, Marco Vianello

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2008435

zbMATH Keywords

algorithmnumerical examplescylinder functionsspecial functionsBessel functionsreal zeros of solutionsKummer's equationoscillatory caseasymptotic and numerical approximation of zeros

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Numerical computation of solutions to single equations (65H05) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Numerical methods for ordinary differential equations (65L99)

Related Items (8)

Improved estimates for the derivatives of the \(O\)-symbols in view of numerical applications ⋮ On the existence of nonoscillatory phase functions for second order ordinary differential equations in the high-frequency regime ⋮ Phase function methods for second order linear ordinary differential equations with turning points ⋮ Phase function methods for second order inhomogeneous linear ordinary differential equations ⋮ The ``phase function method to solve second-order asymptotically polynomial differential equations ⋮ Asymptotic-numerical approximations for highly oscillatory second-order differential equations by the phase function method ⋮ On the asymptotics of Bessel functions in the Fresnel regime ⋮ WKBJ-type approximation for finite moments perturbations of the differential equation \(y\)=\(0\) and the analogous difference equation

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