Biomedical subjects

Joshua Wilkie

Publications and source records attributed to Joshua Wilkie.

3 recordsLinked to original sources

PubMed2004

Numerical methods for stochastic differential equations.

Stochastic differential equations (SDE's) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes for solving stochastic equations is outlined here. High-order numerical methods are developed for the integration of stochastic differential equations with strong solutions. We demonstrate the accuracy of the resulting integration schemes by computing the errors in approximate solutions for SDE's which have known exact solutions.

Journal Article↗

PubMed2003

Numerical method for integrodifferential generalized Langevin and master equations.

We show that the integrodifferential generalized Langevin and non-Markovian master equations can be transformed into larger sets of ordinary-differential equations. On the basis of this transformation we develop a numerical method for solving such integrodifferential equations. Physically motivated example calculations are performed to demonstrate the accuracy and convergence of the method.

Journal Article↗

PubMed2003

Variational principle for stochastic wave and density equations.

We develop a stochastic generalization of the McLachlan variational principle and show that it can be used to derive known stochastic wave equations. We then use it to obtain an exact probability preserving stochastic density decomposition for vibrational dynamics problems with pairwise interaction.

Journal Article↗