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math.NA2026★ 1 cited
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…
math.NA2024
Algebraic Conditions for Stability in Runge-Kutta Methods and Their Certification via Semidefinite Programming
Austin Juhl, David Shirokoff
In this work, we present approaches to rigorously certify - and -stability in Runge-Kutta methods through the solution of convex feasibility problems defined by linear ma…
math.NA2024
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…