Explicit Finite Difference Approximation Research Articles

The stability of finite difference approximations to second order linear parabolic differential equations

Abstract : Explicit finite difference approximations to the initial value problem for a second order linear parabolic differential equation with variable coefficients in two independent variables are considered. Essentially, our problem is to determine conditions which will guarantee that the approximating difference problem is well-posed. Since we deal with explicit difference equations the existence of a unique solution of the difference problem is trivial. Thus our main concern is the dependence of the solution of the difference problem on its data. Roughly speaking, a difference problem is said to be stable if its solution depends continuously on the data, uniformly for all sufficiently fine lattices of mesh points. (Author)