On the choice of initial conditions of difference schemes for parabolic equations

Abstract

AbstractWe study finite difference schemes to approximate the first initial‐boundary value problem for linear second order parabolic equations and obtain some convergence rate estimates. When difference schemes are constructed for such problems, in the process of obtaining convergence rate estimates compatible with smoothness of the solution, various authors assume that the solution of the problem can be extended to the exterior of the domain of integration, preserving the Sobolev class. Our investigations show that this restriction can be removed if, instead of using the exact initial condition, we use certain approximations of the initial conditions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)