A second-order Magnus-type integrator for quasi-linear parabolic problems
نویسندگان
چکیده
منابع مشابه
A second-order Magnus-type integrator for quasi-linear parabolic problems
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 ...
متن کاملConvergence analysis of high-order commutator-free quasi-Magnus exponential integrators for non-autonomous linear evolution equations of parabolic type
The main objective of this work is to provide a stability and error analysis of high-order commutator-free quasi-Magnus (CFQM) exponential integrators. These time integration methods for non-autonomous linear evolution equations are formed by products of exponentials involving linear combinations of the defining operator evaluated at certain times. In comparison with other classes of time integ...
متن کاملOrder-type existence theorem for second order nonlocal problems at resonance
This paper gives an abstract order-type existence theorem for second order nonlocal boundary value problems at resonance and obtain existence criteria for at least two positive solutions, where $f$ is a continuous function. Our results generalize or extend related results in the literature and give a positive answer to the question raised in the literature. An example is given to illustr...
متن کاملA second-order positivity preserving scheme for semilinear parabolic problems
In this paper we study the convergence behaviour and geometric properties of Strang splitting applied to semilinear evolution equations. We work in an abstract Banach space setting that allows us to analyse a certain class of parabolic equations and their spatial discretizations. For this class of problems, Strang splitting is shown to be stable and second-order convergent. Moreover, it is show...
متن کاملHigher-Order Exponential Integrators for Quasi-Linear Parabolic Problems. Part I: Stability
Explicit exponential integrators based on general linear methods are studied for the time discretization of quasi-linear parabolic initial-boundary value problems. Compared to other exponential integrators encountering rather severe order reductions, in general, the considered class of exponential general linear methods provides the possibility to construct schemes that retain higher-order accu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2007
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-06-01883-7