Asymptotic solutions of inhomogeneous differential equations having a turning point
T. M. Dunster
Abstract
Abstract Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The asymptotic approximations are uniformly valid for unbounded complex values of the argument, and are applied to inhomogeneous Airy equations having polynomial and exponential forcing terms. Error bounds are available for all approximations, including new simple ones for the well‐known asymptotic expansions of Scorer functions of large complex argument.
Topics & Concepts
Airy functionMethod of matched asymptotic expansionsSimple (philosophy)MathematicsPolynomialExponential functionMathematical analysisAsymptotic analysisDifferential equationForcing (mathematics)Turning pointArgument (complex analysis)Point (geometry)Asymptotic analysisApplied mathematicsPhysicsGeometryEpistemologyChemistryBiochemistryPhilosophyAcousticsPeriod (music)Mathematical functions and polynomialsScientific Research and DiscoveriesNumerical methods for differential equations