Continuous numerical methods for ODEs with defect control

Numerical methods for the 2nd moment of stochastic ODEs

Numerical methods for stochastic ordinary differential equations typically estimate moments of the solution from sampled paths. Instead, in this paper we directly target the deterministic equation satisfied by the first and second moments. For the canonical examples with additive noise (Ornstein–Uhlenbeck process) or multiplicative noise (geometric Brownian motion) we derive these deterministic...

high order second derivative methods with runge--kutta stability for the numerical solution of stiff odes

‎we describe the construction of second derivative general linear methods (sglms) of orders five and six‎. ‎we will aim for methods which are a--stable and have runge--kutta stability property‎. ‎some numerical results are given to show the efficiency of the constructed methods in solving stiff initial value problems‎.

Parallel methods for ODEs

In recent years there has been considerable interest in exploiting parallel computers for the efficient solution of ordinary differential equations. Because initial value problems are by their very nature sequential it can require considerable ingenuity to construct and implement efficient methods which take advantage of parallelism (see, for example, the monograph of Burrage (Oxford University...

PMIRKDC: a parallel mono-implicit Runge-Kutta code with defect control for boundary value ODEs

We describe parallel software, PMIRKDC, for solving boundary value ordinary differential equations (BVODEs). This software is based on the package, MIRKDC, which employs monoimplicit Runge-Kutta schemes within a defect control algorithm. The primary computational costs involve the treatment of large, almost block diagonal (ABD) linear systems. The most significant feature of PMIRKDC is the repl...

Numerical Solution of ODEs with Distributed Maple