Module esdirk 

ESDIRK: Explicit first Stage, Singly Diagonally Implicit Runge-Kutta methods.

ESDIRK methods are efficient implicit methods for stiff ODEs. They have the property that all implicit stages share the same diagonal coefficient, allowing efficient Jacobian reuse.

Available Methods

• Esdirk32 - ESDIRK2(1)3L[2]SA: 3-stage, 2nd order (A-stable, L-stable)
• Esdirk43 - ESDIRK3(2)4L[2]SA: 4-stage, 3rd order (A-stable, L-stable)
• Esdirk54 - ESDIRK4(3)6L[2]SA: 6-stage, 4th order (L-stable, stiffly-accurate)

Reference

• Kennedy, C.A. & Carpenter, M.H. (2016), “Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review”, NASA/TM-2016-219173.

Author: Moussa Leblouba Date: 5 March 2026 Modified: 2 May 2026

Structs

Esdirk32

ESDIRK3(2): 3-stage, 2nd order ESDIRK method.

Esdirk43

ESDIRK4(3): 4-stage, 3rd order ESDIRK method.

Esdirk54

ESDIRK5(4): 6-stage, 4th order ESDIRK method (L-stable, stiffly-accurate).