An improved class of generalized Runge-Kutta methods for stiff problems. I: The scalar case
The authors present a new family of \(p\)-stage methods for the numerical integration of some scalar ordinary differential equations (ODEs). The method provides better order and stability results and may be viewed as a generalization of explicit \(p\)-stage Runge-Kutta methods. Explicit \(A\)-stable and \(L\)-stable methods for the numerical integration of scalar autonomous ODEs are obtained at the cost of losing linearity in the formulas. This method is generalized to work for non-autonomous scalar ODEs and systems in a subsequent work. Numerical examples are given to demonstrate the effectiveness of the method.
explicit \(p\)-stage Runge-Kutta methods
scientific article; zbMATH DE number 1861141
scientific article