Runge-Kutta methods for linear ordinary differential equations
Spatial discretizations of linear partial differential equations lead to systems of ordinary differential equations of the form \(u'=Au-g(t)\). This motivates the authors to construct new explicit \(4\)-, \(5\)-, and \(6\)-stage Runge-Kutta methods, which are \(3\)rd order accurate for nonlinear problems, but for problems of the form \(u'=Au-g(t)\) they are of order \(4\), \(5\), and \(6\), respectively. The stability polynomials of the new methods coincide with the truncated Taylor series of \(\exp z\).
scientific article; zbMATH DE number 1367742