Discretisation of abstract linear evolution equations of parabolic type
Fernando F. Gonçalves, Maria do Rosário Grossinho, Eva Morais · Advances in Difference Equations · 2012
We investigate the discretisation of the linear parabolic equation du/dt = A(t)u + f(t) in abstract spaces, making use of both the implicit and the explicit finite-difference schemes.The stability of the explicit scheme is obtained, and the schemes' rates of convergence are estimated.Additionally, we study the special cases where A and f are approximated by integral averages and also by weighted arithmetic averages.MSC 2010: 65J10.