Solution of the Pontriagin–Vitt equation for the moments of time to first passage of the randomly accelerated particle by the finite element method

✍ Scribed by L. A. Bergman; J. C. Heinrich

• Publisher: John Wiley and Sons
• Year: 1980
• Tongue: English
• Weight: 196 KB
• Volume: 15
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620150913

✦ Synopsis

Abstract

The Pontriagin–Vitt equation governing the mean of the time of first passage of a randomly accelerated particles has been studied extensively by Franklin and Rodemich.^1^ In their paper is presented the analytic solution for the two‐sided barrier problem and solutions by several finite difference procedures.

This note demonstrates solution of the problem by a Petrov–Galerkin finite element method using upstream weighting functions,^2^ shown to give rapidly convergent results. In addition, the equation is generalized to include higher statistical moments, and solutions for the first few ordinary moments are reported.