\(A_ 0\)-contractivity of the variable-step BDF's of order less than four
The author investigates the stability of the variable-step, variable- order backward differentiation formulas (BDF's), when applied to stiff differential equations. For \(y'=\lambda (t,y)y\) with real non-positive \(\lambda\) (t,y) it is shown that the numerical solution remains bounded for arbitrarily large stepsizes, provided that the stepsize-ratios satisfy some (very strong) restrictions. These restrictions were derived by a formula manipulation system.
variable-step, variable-order backward differentiation formulas
scientific article; zbMATH DE number 3915556