Stochastic methods for solving highdimensional partial differential equations
Abstract
We propose algorithms for solving highdimensional Partial Differential Equations (PDEs) that combine a probabilistic interpretation of PDEs, through FeynmanKac representation, with sparse interpolation. MonteCarlo methods and timeintegration schemes are used to estimate pointwise evaluations of the solution of a PDE. We use a sequential control variates algorithm, where control variates are constructed based on successive approximations of the solution of the PDE. Two different algorithms are proposed, combining in different ways the sequential control variates algorithm and adaptive sparse interpolation. Numerical examples will illustrate the behavior of these algorithms.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.05423
 Bibcode:
 2019arXiv190505423B
 Keywords:

 Mathematics  Numerical Analysis