Gonçalves, Fernando F.Grossinho, Maria do RosárioEva, Morais2023-04-172023-04-172012Gonçalves, Fernando F., Maria do Rosário Grossinho and Eva Morais . (2012). “Discretisation of abstract linear evolution equations of parabolic type”. Advances in Difference Equations Vol. 1: pp 1-29.http://hdl.handle.net/10400.5/27632We 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.engParabolic Evolution EquationsFinite-difference MethodsFinancial Mathematicsjournal article