Abstract
If P
j
(z)/P
j
(−z) is the (j,j)-diagonal Padé approximation to exp(z), we show that those numerical methods for y″ = f(t
y) which, when applied to the test equation have associated characteristic polynomial
are not P-stable in the sense of Lambert and Watson [1] except for j=1 (the trapezoidal rule). Further, we show that for j≧2 the size of the interval of periodicity of such a method does not exceed 12 and for j→ ∞ it decreases down to π2. Our present investigation has been motivated by a result noted to the contrary in [3].