1 citations · 2 across the 4 of their papers we have counts for
4 papers
Adaptive Diagonally Implicit Runge-Kutta Methods Devoid of Order Reduction for Semilinear ODEs
Steven B. Roberts, Abhijit Biswas, David Shirokoff +1
Diagonally implicit Runge-Kutta (DIRK) methods are a prominent class of numerical methods for solving stiff systems of ordinary differential equations (ODEs). Stiffness does not on…
Leveraging higher-order time integration methods for improved computational efficiency in a rainshaft model
Justin Dong, Sean P. Santos, Steven B. Roberts +2
Cloud and precipitation microphysics packages in atmospheric general circulation models typically use first-order time integration methods with a large time step, requiring ad hoc…
A Stiff Order Condition Theory for Runge-Kutta Methods Applied to Semilinear ODEs
Steven B. Roberts, David Shirokoff, Abhijit Biswas +1
Classical convergence theory of Runge-Kutta methods assumes that the time step is small relative to the Lipschitz constant of the ordinary differential equation (ODE). For stiff pr…
Explicit Runge Kutta Methods that Alleviate Order Reduction
Abhijit Biswas, David I. Ketcheson, Steven Roberts +2
Explicit Runge--Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to initial-boundary value problem with time-dependent boundary c…