Exact and fast numerical algorithms for the stochastic wave equation

Exact and fast numerical algorithms for the stochastic wave equation

On the basis of integral representations we propose fast numerical methods to solve the Cauchy problem for the stochastic wave equation without boundaries and with the Dirichlet boundary conditions. The algorithms are exact in a probabilistic sense. 1 Statement of the problem and integral representations Consider the stochastic wave equation ∂X ∂t (t, x)− a2 X ∂x (t, x) = g(t, x) + f(t, x) dW (...

Exact Controllability for a Nonlinear Stochastic Wave Equation

Numerical exact controllability of the 1D heat equation: dual algorithms

This work addresses the numerical approximation of distributed null controls (with small support) for the 1D heat equation, with Dirichlet boundary conditions: the goal is to compute a control that drives the solution from a prescribed initial state at t = 0 to zero at t = T . The earlier contribution by Carthel, Glowinski and Lions [3] considers boundary controls and exhibits numerical instabi...

Fast quantum algorithms for numerical integrals and stochastic processes1

We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct a p proaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algorithms and a quadratic speed increase in comparison to classical Monte Carlo (probabilistic) methods. We derive a simpler and slightl...

Fast quantum algorithms for numerical integrals and stochastic processes

We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known classical deterministic algorithms and a quadratic speed increase in comparison to classical Monte Carlo (probabilistic) methods. We derive a simpler and slightly ...