A Stable and Accurate Explicit Scheme for Parabolic Evolution Equations

APPROXIMATION OF STOCHASTIC PARABOLIC DIFFERENTIAL EQUATIONS WITH TWO DIFFERENT FINITE DIFFERENCE SCHEMES

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.

A High Order Finite Dierence Method for Random Parabolic Partial Dierential Equations

In this paper, for the numerical approximation of random partial differential equations (RPDEs) of parabolic type, an explicit higher order finite difference scheme is constructed. In continuation the main properties of deterministic difference schemes, i.e. consistency, stability and convergency are developed for the random cases. It is shown that the proposed random difference scheme has thes...

A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation

Abstract: We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-elliptic correspondence, we shall derive a two stage iterative procedure employing a fractiona...

Stable Explicit Time Marching in Well-Posed or Ill-Posed Nonlinear Parabolic Equations

This paper analyzes an effective technique for stabilizing pure explicit time dif­ ferencing in the numerical computation of multidimensional nonlinear parabolic equations. The method uses easily synthesized linear smoothing operators at each time step to quench the instabil­ ity. Smoothing operators based on positive real powers of the negative Laplacian are helpful, and (−Δ)p can be realized ...

WELL- POSEDNESS OF THE ROTHE DIFFERENCE SCHEME FOR REVERSE PARABOLIC EQUATIONS