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Discretisation of abstract linear evolution equations of parabolic type. (English) Zbl 1278.65078

Summary: 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:

65J10 Numerical solutions to equations with linear operators
39A12 Discrete version of topics in analysis
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