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Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees
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Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees
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Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees
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Journal Article
Numerical solution of the modified and non-Newtonian Burgers equations by stochastic coded trees
2023
Overview
We present the numerical application of a meshfree algorithm for the solution of fully nonlinear PDEs by Monte Carlo simulation using branching diffusion trees coded by the nonlinearities appearing in the equation. This algorithm is applied to the numerical solution of modified and non-Newtonian Burgers equations, and to a problem with boundary conditions in fluid dynamics, by the computation of a Poiseuille flow. Our implementation uses neural networks that yield a functional space-time domain estimation, and includes numerical comparisons with the deep Galerkin (DGM) and deep backward stochastic differential equation (BSDE) methods.
Publisher
Springer Japan,Springer Nature B.V
