On accuracy and unconditional stability of linear multistep methods for second order differential equations

Linear multistep methods for solution of the equationy=f(t, y) are studied by means of the test equationy=–²y, with real. It is shown that the order of accuracy cannot exceed 2 for an unconditionally stable method.This work was supported by the NASA-Ames Research Center, Moffett Field, California, under Interchange No. NCA2-OR745-712, while the author was a visitor at the Computer Science Department, Stanford University, Stanford, California.