Stability of Numerical Methods for Ordinary Differential Equations

Abstract

Variable stepsize stability results are found for three representative multivalue methods. For the second order BDF method, a best possible result is found for a maximum stepsize ratio that will still guarantee A(0)-stability behaviour. It is found that under this same restriction, A(α)-stability holds for α≈70°. For a new two stage two value first order method, which is L-stable for constant stepsize, A(0)-stability is maintained for stepsize ratios as high as aproximately 2.94. For the third order BDF method, a best possible result of (1/2)(1+$\sqrt {\text{5}}$) is found for a ratio bound that will still guarantee zero-stability.