Summation-by-parts in time

DOI10.1016/j.jcp.2013.05.042zbMath1349.65399OpenAlexW2022981527MaRDI QIDQ347987

Tomas Lundquist, Jan Nordström

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2013.05.042

zbMATH Keywords

stabilityconvergenceboundary conditionsinitial value problemstime integrationstiff problemsglobal methodshigh order accuracysummation-by-parts operatorsinitial value boundary problems

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Discrete version of topics in analysis (39A12) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical summation of series (65B10)

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Uses Software

• MEBDF

Cites Work

• Unnamed Item
• Unnamed Item
• Verification of variable-density flow solvers using manufactured solutions
• Stepsize restrictions for boundedness and monotonicity of multistep methods
• Interaction of waves with frictional interfaces using summation-by-parts difference operators: weak enforcement of nonlinear boundary conditions
• Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations
• The integration of stiff initial value problems in ODEs using modified extended backward differentiation formulae
• Fourth-order Runge-Kutta schemes for fluid mechanics applications
• Stable Robin solid wall boundary conditions for the Navier-Stokes equations
• Conservative finite difference formulations, variable coefficients, energy estimates and artificial dissipation
• A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions
• A stable and high-order accurate conjugate heat transfer problem
• Legendre-Gauss collocation methods for ordinary differential equations
• A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
• High-order accurate computations for unsteady aerodynamics
• A stable and conservative interface treatment of arbitrary spatial accuracy
• Summation by parts for finite difference approximations for \(d/dx\)
• Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes
• Initial value problems: Numerical methods and mathematics
• High order finite difference approximations of electromagnetic wave propagation close to material discontinuities
• On coordinate transformations for summation-by-parts operators
• Modified extended backward differentiation formulae for the numerical solution of stiff initial value problems in ODEs and DAEs
• Additive Runge-Kutta schemes for convection-diffusion-reaction equations
• Summation by parts operators for finite difference approximations of second derivatives
• Stiffness in numerical initial-value problems
• Legendre-Gauss-Radau collocation method for solving initial value problems of first order ordinary differential equations
• Conjugate heat transfer for the unsteady compressible Navier-Stokes equations using a multi-block coupling
• A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions
• Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
• IMEX extensions of linear multistep methods with general monotonicity and boundedness properties
• Simulation of dynamic earthquake ruptures in complex geometries using high-order finite difference methods
• Superconvergent functional output for time-dependent problems using finite differences on summation-by-parts form
• On the impact of boundary conditions on dual consistent finite difference discretizations
• Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations
• On monotonicity and boundedness properties of linear multistep methods
• On Order Reduction for Runge–Kutta Methods Applied to Differential/Algebraic Systems and to Stiff Systems of ODEs
• Error Bounded Schemes for Time-dependent Hyperbolic Problems
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• Global integration of differential equations through Lobatto quadrature
• Numerical Methods for Ordinary Differential Equations
• General linear methods for stiff differential equations
• A method for global approximation of the initial value problem