Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
An optimal Runge-Kutta method for steady-state solutions of hyperbolic systems
SIAM Journal on Numerical Analysis
A Hybrid GMRES algorithm for nonsymmetric linear systems
SIAM Journal on Matrix Analysis and Applications
Improved convergence to the steady state of the Euler equations by enhanced wave propagation
Journal of Computational Physics
Analysis of Preconditioners for Hyperbolic Partial Differential Equations
SIAM Journal on Numerical Analysis
Iterative methods for solving linear systems
Iterative methods for solving linear systems
On the adaptive control of a class of SISO dynamic hybrid systems
Applied Numerical Mathematics
On the adaptive control of a class of SISO dynamic hybrid systems
Applied Numerical Mathematics
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Runge–Kutta time integration is used to reach the steady state solution of discretized partial differential equations. Continuous and discrete parameters in the method are adapted to the particular problem by minimizing the residual in each step, if this is possible, or the work to reach convergence. Algorithms for parameter optimization are devised and analyzed. Solutions of the linearized Euler equations and the nonlinear Euler and Navier–Stokes equations for compressible flow illustrate the methods.