Efficient implementation of a 2nd derivative method for stiff ODEs (Q1335470)

Padé or Obrechkoff methods based on diagonal or sub-diagonal Padé approximations for the exponential function usually yield high accuracy and good stability. But the occurrence of higher derivatives makes their implementation difficult. For a third-order sub-diagonal second derivative method, the authors suggest an effective procedure for moderately large, strongly stiff systems under moderate accuracy requirements. They consider a numerical example to illustrate their point.