A note on stability of a three-stage difference scheme for ordinary differential equations
A three-stage difference technique for ordinary differential equations is described. It consist of three implicit steps performed by using either the trapezoidal or the mid-point rule with proper step sizes. The fourth order accuracy of these schemes is derived from the general theory based on a Lie series and the concept of self-adjoint operators. The stability analysis of the three-stage schemes is presented. It is shown that though the scheme is not \(A\)-stable, the instability region in the complex plane is a little disc on the real axis thus providing stability for systems which have eigenvalues not very adjacent to the real axis. Numerical tests for Hamiltonian systems and stiff systems of ordinary differential equations are described to show the accuracy and the stability of the schemes.
scientific article; zbMATH DE number 120307