3 papers
math.NA2026
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…
physics.ao-ph2026
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…
math.NA2025
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…