We introduce and analyze a new finite-difference scheme, relying on the theta-method, for solving monotone second-order mean field games. These games consist of coupled system Fokker–Planck Hamilton–Jacobi–Bellman equation. The theta-method is used discretizing diffusion terms: we approximate them with convex combination an implicit explicit term. On contrast, use centered scheme first-order te...

Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods based on the well-known MAC scheme produce accurate solutions and numerical convergence can be demonstrated using a resolution study, rigorous proofs are usually limited to particular reformulations boundary conditions. In this paper, error analysis o...

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order Report Title In this paper, spatially high-order Residual-Distribution (RD) schemes using the firstorder hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advectiondiffusion scheme was first intro...