The Modified Newton Method in the Solution of Stiff Ordinary Differential Equations
From MaRDI portal
Publication:3361822
DOI10.2307/2938711zbMath0734.65060OpenAlexW4246182060MaRDI QIDQ3361822
Publication date: 1991
Full work available at URL: https://doi.org/10.2307/2938711
convergencestiff systemmodified Newton methodimplicit Runge- Kutta methodsimplicit multistep methods
Numerical computation of solutions to systems of equations (65H10) Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Multiple scale methods for ordinary differential equations (34E13)
Related Items
The use of Butcher series in the analysis of Newton-like iterations in Runge-Kutta formulas ⋮ Simulation of surface-plasma interaction with high surface conductivity ⋮ The effect of the stopping of the Newton iteration in implicit linear multistep methods ⋮ A note on approximate Jacobians of implicit Runge-Kutta methods and convergence of modified Newton iterations ⋮ Two methods for the implicit integration of stiff reaction systems ⋮ A time-filtering method for plasma simulation: high bulk conductivity ⋮ Solving the systems of equations arising in the discretization of some nonlinear p.d.e.'s by implicit Runge-Kutta methods ⋮ On the use of parallel processors for implicit Runge-Kutta methods
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Efficient estimation of sparse Jacobian matrices by differences
- Error bounds for the solution to the algebraic equations in Runge-Kutta methods
- Feasibility and contractivity in implicit Runge-Kutta methods
- A necessary condition for BSI-stability
- Relaxed Newton-like methods for stiff differential systems
- Suitability of Runge-Kutta methods
- Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations
- On the solvability of the systems of equations arising in implicit Runge- Kutta methods
- Stability of implicit Runge-Kutta methods for nonlinear stiff differential equations
- On the D-suitability of implicit Runge-Kutta methods
- A-stable one-step methods with step-size control for stiff systems of ordinary differential equations
- On the equivalence of BS-stability and B-consistency
- On the existence of solutions to the algebraic equations in implicit Runge-Kutta methods
- On conditions for the existence and uniqueness of solutions to the algebraic equations in Runge-Kutta methods
- On the Existence of Solutions for Algebraically Stable Runge—Kutta Methods
- On the Efficient Implementation of Implicit Runge-Kutta Methods
- A User’s View of Solving Stiff Ordinary Differential Equations
- Jacobian Matrix Properties and Their Impact on Choice of Software for Stiff ODE Systems
- Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
- Displacement or Residual Test in the Application of Implicit Methods for Stiff Problems
- On the Algebraic Equations in Implicit Runge–Kutta Methods
- Towards efficient implementation of singly-implicit methods
- On the Parallel Implementation of Implicit Runge–Kutta Methods
- Evaluation of implicit formulas for the solution of ODEs
- An implementation of singly-implicit Runge-Kutta methods
- Implementation of Implicit Formulas for the Solution of ODE<scp>s</scp>
- Modified Diagonally Implicit Runge–Kutta Methods
- Implementation of Rosenbrock Methods
- Type-Insensitive ODE Codes Based on Implicit A(α)-Stable Formulas
- Comparing numerical methods for stiff systems of O.D.E:s
- Some Properties of Algorithms for Stiff Differential Equations
- Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations
- Difference Methods for Stiff Ordinary Differential Equations
- Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
