Order Reduction of Exponential Runge--Kutta Methods: Fourth-Order Schemes for Non-Commuting Operators

Thi Tam Dang, Pablo Alexei Gazca-Orozco, Trung Hau Hoang

This paper extends the convergence analysis of explicit exponential Runge--Kutta methods for linear parabolic problems $u^{\prime }(t)+Au(t)=Bu(t)$, where $A$ generates an analytic semi…