Runge-Kutta approximation of quasi-linear parabolic equations
نویسندگان
چکیده
منابع مشابه
Runge - Kutta Approximation of Quasi - Linear Parabolic Equations
We study the convergence properties of implicit Runge-Kutta methods applied to time discretization of parabolic equations with timeor solutiondependent operator. Error bounds are derived in the energy norm. The convergence analysis uses two different approaches. The first, technically simpler approach relies on energy estimates and requires algebraic stability of the RungeKutta method. The seco...
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Maŕıa López-Fernández1, Christian Lubich2, Cesar Palencia1, and Achim Schädle3 1 Departamento de Matemática Aplicada y Computación, Universidad de Valladolid, Valladolid, Spain. E-mail: {marial, palencia}@mac.cie.uva.es 2 Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D–72076 Tübingen, Germany. E-mail: [email protected] 3 ZIB Berlin, Takustr. 7, D-14195 Berlin,...
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We study the stability of explicit Runge-Kutta methods for high order Lagrangian finite element approximation of linear parabolic equations and establish bounds on the largest eigenvalue of the system matrix which determines the largest permissible time step. A bound expressed in terms of the ratio of the diagonal entries of the stiffness and mass matrices is shown to be tight within a small fa...
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We study the approximation properties of Runge-Kutta time discretizations of linear and semilinear parabolic equations, including incompressible Navier-Stokes equations. We derive asymptotically sharp error bounds and relate the temporal order of convergence, which is generally noninteger, to spatial regularity and the type of boundary conditions. The analysis relies on an interpretation of Run...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1995
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1995-1284670-0