Optimal orders of convergence for Runge-Kutta methods and linear, initial boundary value problems

DOI10.1016/S0168-9274(02)00110-1zbMath1020.65057OpenAlexW1965251554MaRDI QIDQ1861971

Isaías Alonso-Mallo, César Palencia

Publication date: 10 March 2003

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

Full work available at URL: https://doi.org/10.1016/s0168-9274(02)00110-1

zbMATH Keywords

Banach spacessemigroupsnumerical experimentsinitial boundary value problemsRunge-Kutta methodspartial differential equationsoptimal orderfractional orders

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Linear differential equations in abstract spaces (34G10)

Related Items (14)

Analysis of order reduction when integrating linear initial boundary value problems with Lawson methods ⋮ Runge-Kutta time semidiscretizations of semilinear PDEs with non-smooth data ⋮ Spectral-fractional step Runge–Kutta discretizations for initial boundary value problems with time dependent boundary conditions ⋮ Runge-Kutta approximation for \(C_0\)-semigroups in the graph norm with applications to time domain boundary integral equations ⋮ Time domain boundary integral equations and convolution quadrature for scattering by composite media ⋮ Comparison of efficiency among different techniques to avoid order reduction with Strang splitting ⋮ Avoiding order reduction phenomenon for general linear methods when integrating linear problems with time dependent boundary values ⋮ Design of DIRK schemes with high weak stage order ⋮ Algebraic Structure of the Weak Stage Order Conditions for Runge–Kutta Methods ⋮ Higher-order temporal integration for the incompressible Navier-Stokes equations in bounded domains ⋮ Order reduction and how to avoid it when explicit Runge-Kutta-Nyström methods are used to solve linear partial differential equations ⋮ Time-domain boundary integral equation modeling of heat transmission problems ⋮ Spectral/Rosenbrock discretizations without order reduction for linear parabolic problems ⋮ Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems

Cites Work

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• A Stability Result for Sectorial Operators in Banach Bpaces
• Avoiding the order reduction of Runge-Kutta methods for linear initial boundary value problems
• Single step methods for inhomogeneous linear differential equations in Banach space
• Runge-Kutta Methods for Partial Differential Equations and Fractional Orders of Convergence
• On Rational Approximations of Semigroups
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• Stability of Rational Multistep Approximations of Holomorphic Semigroups
• On the convolution operators arising in the study of abstract initial boundary value problems
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