On integration of quasi-linear parabolic equations by explicit difference methods
نویسندگان
چکیده
منابع مشابه
Fully implicit, linearly implicit and implicit-explicit backward difference formulae for quasi-linear parabolic equations
Quasi-linear parabolic equations are discretised in time by fully implicit backward difference formulae (BDF) as well as by implicit–explicit and linearly implicit BDF methods up to order 5. Under appropriate stability conditions for the various methods considered, we establish optimal order a priori error bounds by energy estimates, which become applicable via the Nevanlinna-Odeh multiplier te...
متن کاملFinite Element Methods for Optimal Control Problems Governed by Linear Quasi-parabolic Integro-differential Equations
Linear quasi-parabolic integro-differential equations and their control appear in many scientific problems and engineering applications such as biology mechanics, nuclear reaction dynamics, heat conduction in materials with memory, and visco-elasticity, etc.. The existence and uniqueness of the solution of the linear quasi-parabolic integro-differential equations have been studied by Wheeler M....
متن کاملOn Third-order Linear Difference Equations Involving Quasi-differences
had been investigated. As it is noted here, these equations are not adjoint equations and are referred to as quasi-adjoint equations. Equation (E) is a special case of linear nth-order difference equations with quasi-differences. Such equations have been widely studied in the literature, see, for example, [6, 11] and the references therein. The natural question which arises is to find the adjoi...
متن کاملStability of Explicit Runge-Kutta Methods for High Order Finite Element Approximation of Linear Parabolic Equations
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...
متن کاملRunge - 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...
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: Transactions of the American Mathematical Society
سال: 1959
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1959-0141235-6