Implementation of second derivative general linear methods
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Publication:2198185
DOI10.1007/s10092-020-00370-wzbMath1453.65155OpenAlexW3042291837MaRDI QIDQ2198185
Publication date: 9 September 2020
Published in: Calcolo (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10092-020-00370-w
general linear methodslocal error estimationsecond derivative methodsNordsieck techniqueimplementation issues
Numerical methods for initial value problems involving ordinary differential equations (65L05) Software, source code, etc. for problems pertaining to numerical analysis (65-04)
Related Items (15)
Composite symmetric second derivative general linear methods for Hamiltonian systems ⋮ HIGH ORDER EXPLICIT SECOND DERIVATIVE METHODS WITH STRONG STABILITY PROPERTIES BASED ON TAYLOR SERIES CONDITIONS ⋮ Global error estimation for explicit second derivative general linear methods ⋮ Generalized second derivative linear multistep methods for ordinary differential equations ⋮ EXPLICIT NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS FOR ODES ⋮ Recent advances in the numerical solution of Volterra integral equations ⋮ HIGH ORDER SECOND DERIVATIVE DIAGONALLY IMPLICIT MULTISTAGE INTEGRATION METHODS FOR ODES ⋮ Variable stepsize multivalue collocation methods ⋮ RK-stable second derivative multistage methods with strong stability preserving based on Taylor series conditions ⋮ Algebraic stability and irreducibility of second derivative methods ⋮ Strong stability preserving second derivative general linear methods based on Taylor series conditions for discontinuous Galerkin discretizations ⋮ A new one-step method with three intermediate points in a variable step-size mode for stiff differential systems ⋮ Variable stepsize SDIMSIMs for ordinary differential equations ⋮ Parallel-in-time high-order multiderivative IMEX solvers ⋮ Multivalue second derivative collocation methods
Uses Software
Cites Work
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- Construction of high-order quadratically stable second-derivative general linear methods for the numerical integration of stiff ODEs
- Second derivative general linear methods with inherent Runge-Kutta stability
- G-symplectic second derivative general linear methods for Hamiltonian problems
- Applications of order arrows
- Order bounds for second derivative approximations
- Sequential second derivative general linear methods for stiff systems
- An extension of general linear methods
- Maximal order for second derivative general linear methods with Runge-Kutta stability
- On explicit two-derivative Runge-Kutta methods
- Perturbed second derivative multistep methods
- Order and stability of generalized Padé approximations
- Automatic selection of the initial step size for an ODE solver
- A PI stepsize control for the numerical solution of ordinary differential equations
- Diagonally-implicit multi-stage integration methods
- Construction of high order diagonally implicit multistage integration methods for ordinary differential equations
- Diagonally implicit general linear methods for ordinary differential equations
- The construction of practical general linear methods
- Implementation of DIMSIMs for stiff differential systems
- Efficient Nordsieck second derivative general linear methods: construction and implementation
- Towards a code for nonstiff differential systems based on general linear methods with inherent Runge-Kutta stability
- Symmetric second derivative integration methods
- Unconditionally stable general linear methods for ordinary differential equations
- Stiffly stable second derivative multistep methods with higher order and improved stability regions
- Error estimation for Nordsieck methods
- Experiments with a variable-order type 1 DIMSIM code
- Construction of the Nordsieck second derivative methods with RK stability for stiff ODEs
- Implementation of Nordsieck second derivative methods for stiff ODEs
- On the construction of second derivative diagonally implicit multistage integration methods for ODEs
- New second derivative multistep methods for stiff systems
- General linear methods with external stages of different orders
- Second derivative methods with RK stability
- The MATLAB ODE Suite
- Order stars and stability theorems
- Second Derivative Extended Backward Differentiation Formulas for the Numerical Integration of Stiff Systems
- Comparing numerical methods for stiff systems of O.D.E:s
- Control-theoretic techniques for stepsize selection in implicit Runge-Kutta methods
- Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods
- Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations
- CONSTRUCTION OF NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS WITH INHERENT QUADRATIC STABILITY
- Solving Ordinary Differential Equations II
- On the Convergence of Numerical Solutions to Ordinary Differential Equations
- Second Derivative Multistep Methods for Stiff Ordinary Differential Equations
- Numerical Methods for Ordinary Differential Equations
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