Parabolic Cylinder Functions: Examples of Error Bounds for Asymptotic Expansions

Parabolic Cylinder Functions:Examples of Error Bounds For Asymptotic Expansions

Several asymptotic expansions of parabolic cylinder functions are discussed and error bounds for remainders in the expansions are presented. In particular Poincaré-type expansions for large values of the argument z and uniform expansions for large values of the parameter are considered. The expansions are based on those given in [5] and on modifications of these expansions given in [9]. Compute...

Absence of zeros and asymptotic error estimates for Airy and parabolic cylinder functions

Numerical and Asymptotic Aspects of Parabolic Cylinder Functions

Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic expansions given earlier by F.W.J. Olver. Some of his results are modified to improve the asymptotic properties and to enlarge the intervals for using the expansions...

Asymptotic expansions for degenerate parabolic equations

Article history: Received 14 May 2014 Accepted after revision 26 September 2014 Available online 11 October 2014 Presented by Olivier Pironneau We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the unifo...

New POD Error Expressions, Error Bounds, and Asymptotic Results for Reduced Order Models of Parabolic PDEs

The derivations of existing error bounds for reduced order models of time varying partial differential equations (PDEs) constructed using proper orthogonal decomposition (POD) have relied on bounding the error between the POD data and various POD projections of that data. Furthermore, the asymptotic behavior of the model reduction error bounds depends on the asymptotic behavior of the POD data ...