Parallelism across the steps in iterated Runge-Kutta methods for stiff initial value problems
Copyright policy )Parallelism across the steps in iterated Runge-Kutta methods for stiff initial value problems
The paper deals with the solution of the initial value problem: \(y'(t)= f(y(t))\), \(y(t_ 0)= y_ 0\), \(y,f\in \mathbb{R}^ d\) on parallel computers using step-parallel iteration methods. As corrector formula the authors adopt a classical implicit Runge-Kutta formula of Radau IIA type. For the iteration they use a parallel diagonally implicit Runge-Kutta (PDIRK) approach developed by the first two authors earlier. Because in the PDIRK procedure the number of iterations needed is high, the authors introduce preconditioning in order to reduce this number.
- Centrum Wiskunde & Informatica Netherlands
- Dutch Research Council Netherlands
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, stiff initial value problems, preconditioning, iteration methods, parallel diagonally implicit Runge-Kutta approach, Parallel numerical computation, Multiple scale methods for ordinary differential equations, Nonlinear ordinary differential equations and systems, parallel computation, Numerical methods for initial value problems involving ordinary differential equations, Runge-Kutta formula of Radau IIA type
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, stiff initial value problems, preconditioning, iteration methods, parallel diagonally implicit Runge-Kutta approach, Parallel numerical computation, Multiple scale methods for ordinary differential equations, Nonlinear ordinary differential equations and systems, parallel computation, Numerical methods for initial value problems involving ordinary differential equations, Runge-Kutta formula of Radau IIA type
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