Stability of multistep Runge-Kutta methods for systems of functional-differential and functional equations.
The aim of the paper is the stability of multistep Runge-Kutta methods applied to systems of linear functional-differential and functional equations. The first part concerns the problem statement and the principal results existing in the literature concerning the stability of difference formulas for the systems of functional-differential and functional equations. The second part is devoted to the numerical methods, more precisely the multistep Runge-Kutta methods. One presents the numerical process obtained by applying one of these Runge-Kutta methods to the considered system of functional-differential and functional equations presented in the first section. The last part is devoted to the stability analysis of the above numerical process. Some results concerning the relation between the stability of the numerical process and the \(A\)-stability of the numerical Runge-Kutta method which generates this one are presented.
systems of functional-differential and functional equations
scientific article; zbMATH DE number 2138627