Families of two-step fourth order \(P\)-stable methods for second order differential equations
In the numerical integration of initial value problems for second order ordinary differential equations, \textit{J. D. Lambert} and \textit{I. A. Watson} [J. Inst. Math. Appl. 18, 189-202 (1976; Zbl 0359.65060)] introduced the concept of \(P\)-stability as a desirable property for numerical methods to possess. P-stable linear multistep methods suffer from an order barrier of two. This barrier can however be overcome within the class of hybrid methods, as shown, independently, by \textit{M. M. Chawla} [BIT 21, 190-193 (1981; Zbl 0457.65053)] and \textit{J. R. Cash} [Numer. Math. 37, 355-370 (1981; Zbl 0488.65029)], who constructed fourth order, two-step methods which normally require three function evaluations per step. The present contribution shows how an appropriate choice of the free parameters in the Chawla-Cash family can result in computational savings.
scientific article; zbMATH DE number 3967819
scientific article