We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general H initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in terms of the spatial discretization parameter, we prove that the difference scheme converges strongly in H towards a dissipative weak solution of Cam...

in this article, we study the analytical solutions of different parabolic heat equations with different boundaryconditions in the form of multi-term fractional differential equations. then we compare these analytical solutions with numerical finite difference methods. this comparison demonstrates the accuracy of the analytical and numerical methods presented here.

We consider mimetic finite difference approximations to second order elliptic problems on non-matching multi-block grids. Mortar finite elements are employed on the non-matching interfaces to impose weak continuity of the velocity. Optimal convergence and, for certain cases, superconvergence is established for both the scalar variable and the velocity.

we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order difference in nonconforming multiblock fashion. The aim is optimize computational efficiency when complex geometries are present. proposed coupling technique requires minimal changes the existing schemes while maintaining strict stability, accuracy, energy conservation. Results demonstrated on linea...