52 citations · 95 across the 6 of their papers we have counts for
4 papers · 1 filter
Error Bounds for Boundary-Stopped Positive Cubature Schemes for Hamilton--Jacobi--Bellman Equations
Haoran Xu, Xingye Yue
We derive error bounds for a boundary-stopped positive cubature scheme for degenerate parabolic Hamilton--Jacobi--Bellman equations with Dirichlet data on bounded domains. The sche…
A Positivity-Preserving Expectation Scheme for Hamilton--Jacobi--Bellman Equations with Oblique Robin Boundary Conditions
Haoran Xu, Xingye Yue
For anisotropic diffusion with mixed derivatives, standard compact coordinate-aligned stencils and some local finite-volume or finite-element constructions can lose nonnegative coe…
A Non-compact Positivity-Preserving Numerical Scheme for Elliptic Differential Equations Based on Mathematical Expectation
Haoran Xu, Kunyang Li, Xingye Yue
We propose a novel non-compact, positivity-preserving scheme for linear non-divergence form elliptic equations. Based on the Feynman--Kac formula, the solution is represented as a…
A Non-compact Positivity-Preserving Scheme for Parabolic PDE via Conditional Expectation
Haoran Xu, Jie Ren, Xingye Yue
We propose a novel non-compact, positivity-preserving scheme for linear non-divergence form parabolic equations. Based on the Feynman-Kac formula, the solution is expressed as a co…