134 citations · 770 across the 68 of their papers we have counts for
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Very High-Order A-stable Stiffly Accurate Diagonally Implicit Runge-Kutta Methods with Error Estimators
Yousef Alamri, David I. Ketcheson
A numerical search approach is used to design high-order diagonally implicit Runge-Kutta (DIRK) schemes equipped with embedded error estimators, some of which have identical diagon…
A Comparative Study of Iterative Riemann Solvers for the Shallow Water and Euler Equations
Carlos Muñoz Moncayo, Manuel Quezada de Luna, David I. Ketcheson
The Riemann problem for first-order hyperbolic systems of partial differential equations is of fundamental importance for both theoretical and numerical purposes. Many approximate…
Design of DIRK Schemes with High Weak Stage Order
Abhijit Biswas, David Ketcheson, Benjamin Seibold +1
Runge-Kutta (RK) methods may exhibit order reduction when applied to certain stiff problems. While fully implicit RK schemes exist that avoid order reduction via high-stage order,…
Algebraic Structure of the Weak Stage Order Conditions for Runge-Kutta Methods
Abhijit Biswas, David Ketcheson, Benjamin Seibold +1
Runge-Kutta (RK) methods may exhibit order reduction when applied to stiff problems. For linear problems with time-independent operators, order reduction can be avoided if the meth…