Stable difference approximations for parabolic equations

On Difference Schemes for Hyperbolic-Parabolic Equations

The nonlocal boundary value problem for a hyperbolic-parabolic equation in a Hilbert space H is considered. The difference schemes approximately solving this boundary value problem are presented. The stability estimates for the solution of these difference schemes are established. In applications, the stability estimates for the solutions of the difference schemes of the mixed type boundary val...

Difference Schemes for Degenerate Parabolic Equations

Diagonal dominant implicit-difference schemes approximating a porous media type class of multidimensional nonlinear equations are shown to generate semigroups in an approximate l) -space, and the rate of convergence to the semigroup solution in Ll is given. The numerical schemes proposed by Berger et al. in [4] are described and a proof of convergence for the fully discrete algorithms is outlin...

Exact Difference Schemes for Parabolic Equations

The Cauchy problem for the parabolic equation ∂u ∂t = ∂ ∂x ( k (x, t) ∂u ∂x ) + f(u, x, t), x ∈ R, t > 0, u(x, 0) = u0(x), x ∈ R, is considered. Under conditions u(x, t) = X(x)T1(t) + T2(t), ∂u ∂x 6= 0, k(x, t) = k1(x)k2(t), f(u, x, t) = f1(x, t)f2(u), it is shown that the above problem is equivalent to a system of two first-order ordinary differential equations for which exact difference schem...

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

numerics of stochastic parabolic differential equations with stable finite difference schemes

in the present article, we focus on the numerical approximation of stochastic partial differential equations of itˆo type with space-time white noise process, in particular, parabolic equations. for each case of additive andmultiplicative noise, the numerical solution of stochastic diffusion equations is approximated using two stochastic finite difference schemes and the stability and consisten...