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The approximation of y=Ay + B't)y +c(t) by linear multistep methods is studied. It is supposed that the matrix A is real symmetric and negative semidefinite, that the multistep method has an interval of absolute stability [—s, 0], and that h2 II A II < s where h is the time step. A priori error bounds are derived which show that the exponential multiplication factor is of the formexp{r;i||B|||„(rt/!)}, |||B|||„ = max0^,^„h \\B't)\\

Linear multistep methods for stable differential equations 𝑦̈=𝐴𝑦+𝐵(𝑡)𝑦̇+𝑐(𝑡)