Quasi-Monte Carlo simulation of differential equations
-
Aïcha Chouraqui
and
Bachir Djebbar
Abstract
We are interested in the numerical solution of the ordinary differential equation y′(t)=f(t,y(t)) when f is smooth in y but lacks regularity in t. We describe a family of methods akin to the Runge–Kutta family. It involves Monte Carlo simulation of integrals. We focus on third-order schemes which use random samples in dimension three. We give error bounds in terms of the step size and the discrepancy of the set used for the Monte Carlo approximations. We solve a model problem in which f undergoes rapid time variations. It is shown for this example that, by using a quasi-random point set in place of pseudo-random samples, we are able to obtain reduced errors.
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Articles in the same Issue
- Frontmatter
- Monte Carlo algorithm for the Robin boundary conditions in application to solving a model diffusion-recombination problem
- A random cloud algorithm for the Schrödinger equation
- Numerical approximation of BSDEs using local polynomial drivers and branching processes
- Quasi-Monte Carlo simulation of differential equations
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Simulation of Gaussian stationary Ornstein–Uhlenbeck process with given reliability and accuracy in space
C([0,T]) - HMM with emission process resulting from a special combination of independent Markovian emissions
