A(α)-acceptability of pade approximations to function exp (Q)

In this paper, a necessary and sufficient condition of A(a)-acceptability for rational approximations to the functionexp(q) and some sufficient conditions to guarantee A(α)-acceptability of Padé approximations^(R)]_mⁿ (q)\hat R_m^n (q) to the functionexp(q) are given, where a ∈(0,π/2), n≤m,m≥2. Furthermore, it is proved that the condition of A(α)-acceptability of rational approximations toexp(q) is equivalent to the nonnegatively of a real polynomial in interval (−∞,0). Finally, we prove that^(R)]₄¹ (q)\hat R_4^1 (q) is A(π/3)-acceptable. Based on this conclusion, two A(π/3)-stable multiderivative (hybrid) one-step methods are constructed.