A second-order Magnus-type integrator for quasi-linear parabolic problems
نویسندگان
چکیده
In this paper, we consider an explicit exponential method of classical order two for the time discretisation of quasi-linear parabolic problems. The numerical scheme is based on a Magnus integrator and requires the evaluation of two exponentials per step. Our convergence analysis includes parabolic partial differential equations under a Dirichlet boundary condition and provides error estimates in Sobolev spaces. In an abstract formulation the initial boundary value problem is written as an initial value problem on a Banach space X u′(t) = A ( u(t) ) u(t), 0 < t ≤ T, u(0) given, involving the sectorial operator A(v) : D → X with domain D ⊂ X independent of v ∈ V ⊂ X. Under reasonable regularity requirements on the problem, we prove the stability of the numerical method and derive error estimates in the norm of certain intermediate spaces between X and D. Various applications and a numerical experiment illustrate the theoretical results.
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عنوان ژورنال:
- Math. Comput.
دوره 76 شماره
صفحات -
تاریخ انتشار 2007