Stability of a multi-rate method for numerical integration of ODE's
The author assumes that a nonlinear initial value problem can be partitioned into two subsystems according to whether the equations characterize slow or fast responses. Two different explicit Runge-Kutta methods with different stepsizes are combined with an extrapolation of the slow-response approximation to approximate the solution of the two subsystems in tandem. The paper derives sufficient conditions for the scheme to be absolutely stable. If is found that the matrix of the test equation needs to be diagonal dominance determines the size of the stability regions. To establish the result, the author gives a detailed argument which traces the two types of components through the application of the method. After realizing for the stability analysis that the derivative evaluations are representing using a linear homogeneous system, the interested reader will be able to follow the arguments through with a little tenacity and willingness to accomodate the few typographical errors that occur.
scientific article; zbMATH DE number 120315