Avoiding order reduction of fractional step Runge-Kutta discretizations for linear time dependent coefficient parabolic problems.

DOI10.1016/j.apnum.2003.11.006zbMath1043.65109OpenAlexW2066348849MaRDI QIDQ1426335

B. Bujanda, J. C. Jorge, Laura Portero

Publication date: 14 March 2004

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2003.11.006

zbMATH Keywords

algorithmsstabilityconvergenceconsistencynumerical experimentsinitial boundary value problemssemidiscretizationevolutionary problemsparabolic problemsorder reductionfractional step Runge-Kutta methods

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Initial value problems for second-order parabolic equations (35K15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Linear differential equations in abstract spaces (34G10)

Related Items

A generalization of Peaceman-Rachford fractional step method., Modified Douglas splitting methods for reaction-diffusion equations, A unified formulation of splitting-based implicit time integration schemes, GePUP: generic projection and unconstrained PPE for fourth-order solutions of the incompressible Navier-Stokes equations with no-slip boundary conditions, Semi-implicit projection methods for incompressible flow based on spectral deferred corrections., Alternating directions implicit integration in a general linear method framework, Error analysis of explicit partitioned Runge-Kutta schemes for conservation laws

Cites Work

• Convergence and order reduction of Runge-Kutta schemes applied to evolutionary problems in partial differential equations
• Spectral/Rosenbrock discretizations without order reduction for linear parabolic problems
• Runge-Kutta methods without order reduction for linear initial boundary value problems
• Avoiding order reduction of Runge-Kutta discretizations for linear time-dependent parabolic problems
• Rosenbrock Methods for Partial Differential Equations and Fractional Orders of Convergence
• Galerkin/Runge-Kutta Discretizations for Parabolic Equations with Time- Dependent Coefficients
• Runge-Kutta Methods for Partial Differential Equations and Fractional Orders of Convergence
• Approximative methods for nonlinear equations (two approaches to the convergence problem)
• Spectral-fractional step Runge–Kutta discretizations for initial boundary value problems with time dependent boundary conditions
• A New Computational Procedure for A.D.I. Methods
• Stability results for fractional step discretizations of time dependent coefficient evolutionary problems