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math.AP2009★ 1 cited
Accelerated finite difference schemes for second order degenerate elliptic and parabolic problems in the whole space
I. Gyongy, N. Krylov
We give sufficient conditions under which the convergence of finite difference approximations in the space variable of possibly degenerate second order parabolic and elliptic equat…
math.AP2004
An accelerated splitting-up method for parabolic equations
István Gyöngy, Nicolai Krylov
We approximate the solution of the Cauchy problem $$ \frac{\partial}{\partial t} u(t,x)=Lu(t,x)+f(t,x), \quad (t,x)\in(0,T]\times\bR^d, $$ $$ u(0,x)=u_0(x),\quad x\in\bR^d $$ b…