Numerical propagator method solutions for the linear parabolic initial boundary‐value problems

On the base of our numerical propagator method a new finite volume difference scheme is proposed for solution of linear initial‐boundary value problems. Stability of the scheme is investigated taking into account the obtained analytical solution of the initial‐boundary value problems. It is shown that stability restrictions for the propagator scheme become weaker in comparison to traditional semi‐implicit difference schemes. There are some regions of coefficients, for which the elaborated propagator difference scheme becomes absolutely stable. It is proven that the scheme is unconditionally monotonic. Analytical solutions, which are consistent with solubility conditions of the problem are formulated for the case of constant coefficients of parabolic equation by using Green function approach. Solubility of the linear initial‐boundary value problem with Newton boundary conditions containing lower order derivatives is discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)