Journal article
A note on approximate Jacobians of implicit Runge–Kutta methods and convergence of modified Newton iterations
BIT Numerical Mathematics, Vol.63(4), 54
2023
DOI: 10.1007/s10543-023-00994-8
Abstract
We consider the application of implicit Runge–Kutta (IRK) methods to systems of implicit ordinary differential equations (ODEs). We are especially interested in the situation when stiffness arises. We show that the eigenvalues of major families of
A
-stable implicit Runge–Kutta methods are simple and have non-negative real part. We give necessary and sufficient conditions for the invertibility of approximate Jacobians of IRK methods. The main result of this note provides some sufficient conditions to ensure local contractivity, hence convergence, of modified Newton iterations of IRK methods for stiff ODEs with step size conditions independent of stiffness.
Details
- Title: Subtitle
- A note on approximate Jacobians of implicit Runge–Kutta methods and convergence of modified Newton iterations
- Creators
- Laurent O. Jay - University of IowaOlga Sokratova - University of Iowa
- Resource Type
- Journal article
- Publication Details
- BIT Numerical Mathematics, Vol.63(4), 54
- Publisher
- Springer Netherlands
- DOI
- 10.1007/s10543-023-00994-8
- ISSN
- 0006-3835
- eISSN
- 1572-9125
- Language
- English
- Date published
- 2023
- Academic Unit
- Mathematics
- Record Identifier
- 9984503057302771
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