A Qualitative Analysis of Two- and Three-Step Methods for Stable Second Order Systems

Variable‐order variable‐step algorithms for second‐order systems. Part 1: The methods

“…Theorem 2. 3. For (4), any consistent linear 1 -step method for first-order ordinary differential equations is equivalent to method (3) with = 27 -112, (P2 = 7, (p3 = 7 2 and 7 a free parameter.…”

“…The 3-stage method is zero at infinity if and only if $ = 2, $ 2 = 11/6, $6 = 1, in which case equations (1 6 In this case the 3-stage method is equivalent to the classical Houbolt 3-step method for linear homogeneous problems (4). 3 …”

“…For the first-order, 2-stage method, the matrix to be decomposed is M + q 2 C h + q3 Kh2, while for the second-order 3-stage method it is i,blM + $,Ch + $6Kh2 In this case the 3-stage method is equivalent to the classical Houbolt 3-step method for linear homogeneous problems (4). 3…”