A third order two step method and a fourth order two step method for the numerical solution of the vector initial value problem dy ÷ dx =F(y), y( a ) = n can be defined by making evaluations of F similar to those found in a classical Runge-Kutta formula. These two step methods are different from classical Runge-Kutta methods in that evaluations of F made at the previous point are used along with those made at the current point in order to obtain the solution at the next point. If the stepsize is fixed, this use of previous computations makes it possible to obtain the solution at the next point by evaluating F two or three times for the third or fourth order method, respectively. These methods are consistent with the initial value problem and are shown to be convergent with its unique solution under certain restrictions. The local truncation error terms are given. Finally, a few numerical results are presented.

article Share on Stability of a Generalized Corrector Formula Authors: Roger L. Crane Iowa State University, Ames, Iowa Iowa State University, Ames, IowaView Profile , Robert J. Lambert Iowa State University, Ames, Iowa Iowa State University, Ames, IowaView Profile Authors Info & Claims Journal of the ACMVolume 9Issue 1Jan. 1962 pp 104–117https://doi.org/10.1145/321105.321116Published:01 January 1962Publication History 9citation304DownloadsMetricsTotal Citations9Total Downloads304Last 12 Months3Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF