3 edition of Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients found in the catalog.
Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients
by National Aeronautics and Space Administration, Langley Research Center in Hampton, Va
Written in English
|Other titles||Galerkin, Runge Kutta discretizations for parabolic equations with time dependent coefficients.|
|Statement||Stephen L. Keeling.|
|Series||ICASE report -- no. 87-61., NASA contractor report -- 178372., NASA contractor report -- NASA CR-178372.|
|Contributions||Langley Research Center.|
|The Physical Object|
The discontinuous Galerkin method with explicit Runge-Kutta time integration for hyperbolic and parabolic systems with source terms Martien A. Hulsen MEMT 19 time-dependent equations have to be solved. Phelan, Malone & Winter () showed that allowing a weak compressibil-. Numerical time stepping methods for ordinary differential equations, including forward Euler, backward Euler, and multi-step and multi-stage (e.g. Runge-Kutta) methods. The time dependent heat equation (an example of a parabolic PDE), with particular focus on how to treat the stiffness inherent in parabolic PDEs. Method of lines discretizations.
Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial. Fractional step Runge-Kutta methods are a class of additive Runge-Kutta schemes that provide efficient time discretizations for evolutionary partial differential equations. This efficiency is due to appropriate decompositions of the elliptic operator involving the spatial by: 4.
control problems with evolution equations Thomas G. Flaig Abstract In this paper we discuss the use of implicit Runge-Kutta schemes for the time discretiza-tion of optimal control problems with evolution equations. The specialty of the considered discretizations is that the discretizations schemes for the state and adjoint state are chosen. Such quasi-boundary methods were also generalized for solving backward time-dependent and nonlinear parabolic equations, backward time-fractional diffusion problems [30, 59, 62], and backward time-fractional inverse source problem. In the current paper, we focus our discussion on the homogeneous case with constant coefficients, however Author: Jun Liu, Mingqing Xiao.
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Galerkin/Runge-Kutta Discretizations for Parabolic Equations with Time-Dependent Coefficients By Stephen L. Keeling* Dedicated to Professor Eugene Isaacson on the occasion of his 70th birthday Abstract. A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial-boundary value problems with time-dependent coefficients.
Galerkin/Runge-Kutta Discretizations for Parabolic Equations with Time Dependent Coefficients Stephen L. Keeling* Abstract. A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and ana- lyzed for linear parabolic initial boundary value problems with.
GALERKIN/RUNGE-KUTTA DISCRETIZATIONS FOR PARABOLIC EQUATIONS Next, Section 4 deals with (), a variant of the base scheme which incorpo-rates a preconditioned iterative method (PIM) for the time stepping equations ().
Specifically, these equations are solved only approximately at the nth. A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial-boundary value problems with time-dependent coefficients.
Unlike any classical. audio All audio latest This Just In Grateful Dead Netlabels Old Time Radio 78 RPMs and Cylinder Recordings. Live Music Archive.
Top Audio Books & Poetry Community Audio Computers & Technology Music, Arts & Culture News & Public Affairs Non-English Audio Spirituality &. Abstract A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients.
Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order : Stephen L. Keeling. on L2, which enables us to apply implicit Runge–Kutta time discretizations to our parabolic problem. Note that a solution of (6) is also a solution of (5) and the only restriction of our approach is that the initial data of the parabolic problem must belong to D(f)⊂L2 rather than to the full by: 6.
Abstract: A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial-boundary value problems with time-dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order of convergence while significantly avoiding what has been called order reduction.
Galerkin/Runge–Kutta Discretizations for Semilinear Parabolic Equations Article (PDF Available) in SIAM Journal on Numerical Analysis 27(2) April with 31 Reads How we measure 'reads'.
The existence and regularity theory for fully nonlinear parabolic problems has been developed in recent years and is summarized in the monograph .
Whereas the literature on numerical discretizations of semilinear and quasilinear parabolic problems is quite rich, see, e.g., [1,8,10,11,14], not that much is known for the fully nonlinear case. Get this from a library. Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients.
[Stephen Louis Keeling; Langley Research Center.]. Efficient, high-order Galerkin/Runge-Kutta methods are constructed and analyzed for certain classes of parabolic initial boundary-value problems.
In particular, the partial differential equations considered are (1) semilinear, (2) linear with time dependent coefficients, and (3) quasilinear. Optimal. In this paper we study the order reduction, caused by the presence of time dependent boundary conditions, in the integration of linear parabolic probl Cited by: 7.
SIAM Journal on Numerical AnalysisGalerkin/Runge–Kutta Discretizations for Semilinear Parabolic Equations. Higher Order Single Step Fully Discrete Approximations for Second Order Hyperbolic Equations with Time Dependent Coefficients. SIAM Cited by: Abstract.
In the present paper we show that the strategy proposed in  to avoid the order reduction of Runge-Kutta methods when integrating linear initial boundary value problems can be extended to also avoid the order reduction in nonlinear rmore, we see that if the Runge-Kutta method is replaced by an appropriate linearly implicit Runge-Kutta method, this strategy is interesting Author: M.
Calvo, J. de Frutos, J. Novo. The development of Runge-Kutta methods for partial differential equations P.J. van der Houwen cw1, P.O. BoxGB Amsterdam, Netherlands Abstract A widely-used approach in the time integration of initial-value problems for time-dependent partial differential equations (PDEs) is.
Galerkin/Runge-Kutta Discretizations for Parabolic Equations with Time- Dependent Coefficients (pp. ) Stephen L.
Keeling DOI: / () A direct discontinuous Galerkin method for time-fractional diffusion equation with discontinuous diffusive coefficient. Complex Variables and Elliptic Equati () Performance study of the multiwavelet discontinuous Galerkin approach for solving the Green‐Naghdi by: Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients [microform On spurious steady-state solutions of explicit Runge-Kutta schemes [microform] / P.K.
Sweby, H.C. Yee, D. Runge–Kutta methods for ordinary differential equations – p. 5/ With the emergence of stiff problems as an important application area, attention moved to implicit methods. Methods have been found based on Gaussian quadrature. Later this extended to methods related to Radau andFile Size: KB.
Many techniques, exploiting the structure of these systems, have been developed for general ODEs. For spatial discretizations of time-dependent partial differential equations (PDEs) these techniques are in general not sufficient and also the structure arising from spatial discretization has to.
Bujanda B., Jorge J.C. () Fractional Step Runge-Kutta Methods for the Resolution of Two Dimensional Time Dependent Coefficient Convection-Diffusion Problems. In: Vulkov L., Yalamov P., Waśniewski J. (eds) Numerical Analysis and Its Applications. NAA Lecture Notes in Computer Science, vol Springer, Berlin, HeidelbergAuthor: Blanca Bujanda, Juan Carlos Jorge.Runge–Kutta time discretization of parabolic diﬀerential equations on evolving surfaces which yields a stability estimate in the natural time-dependent norms for Runge–Kutta methods Interior estimates for time discretizations of parabolic equations, Appl.
Numer. Math. 18 (),