Abstract:

This report is to analyze stability and convergence of exponential integrators for semi-linear delay differential equations. P- and GP-contractivity of explicit exponential Runge-Kutta methods is studied for linear autonomous delay differential equations. RN- and GRN-stability of explicit exponential Runge-Kutta methods is studied for semi-linear delay differential equations. D-convergence and conditional GDN-stability of exponential Runge-Kutta methods are also studied for semi-linear delay differential equations. Besides, Stiff convergence and conditional DN-stability of explicit exponential Runge-Kutta methods are investigated and the stiff order conditions are derived up to order four.