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Theory and Modern Applications

Table 1 Preservation of oscillation for six methods

From: Oscillation of Runge-Kutta methods for advanced impulsive differential equations with piecewise constant arguments

 

Gauss-Legendre

Radau IA, IIA

Lobatto IIIA, IIIB

Lobatto IIIC

 

(v,v)

(v − 1,v)

(v − 1,v − 1)

(v − 2,v)

a<0

v is odd

v is odd

v is even

v is odd

a>0

v is odd

v is even

v is even

v is odd