MULTISTEP METHODS FOR THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS MADE SELF-STARTING.
Abstract
Milne's method and other similar multistep ones for the approximate solution of differential equations, are not selfstarting. They require the use of known p pivotal points (x sub i, y(x sub i)), i = 0,1, ... , (p-1), where x's are equally spaced and y = y(x) is the solution of the differential equation. Usually these pivotal points are generated through the use of a set of so-called p-point formulas, preferably p being an odd integer. But these p-point formulas are not self-starting either. A rational method is established herein which will make these p-point formulas, and consequently also the multistep methods, self-starting. Subsequently the method is extended to systems of differential equations. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1965
- Accession Number
- AD0616870
Entities
People
- Diran Sarafyan
Organizations
- University of Wisconsin–Madison