Conditional Space-time Stability of Collocation Runge–kutta for Parabolic Evolution Equations
نویسندگان
چکیده
We formulate collocation Runge–Kutta time-stepping schemes applied to linear parabolic evolution equations as space-time Petrov–Galerkin discretizations, and investigate their a priori stability for the parabolic space-time norms, that is the continuity constant of the discrete solution mapping. We focus on collocation based on A-stable Gauss–Legendre and L-stable right-Radau nodes, addressing in particular the implicit midpoint rule and the backward Euler time-stepping schemes. Collocation on Lobatto nodes is analysed as a byproduct. We find through explicit estimates that the continuity constant is controlled in terms of the parabolic CFL number together with a measure of self-duality of the spatial discretization. Numerical observations motivate and illustrate the results.
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