On numerical integration of ordinary differential equations

作者：Arnold Nordsieck · 发表于：Mathematics of Computation · 年份：1962 · DOI：10.1090/s0025-5718-1962-0136519-5 · 被引用次数：403 · 研究领域：Numerical Methods and Algorithms、Numerical methods for differential equations、Modeling and Simulation Systems

A reliable efficient general-purpose method for automatic digital computer integration of systems of ordinary differential equations is described. The method operates with the current values of the higher derivatives of a polynomial approximating the solution. It is thoroughly stable under all circumstances, incorporates automatic starting and automatic choice and revision of elementary interval size, approximately minimizes the amount of computation for a specified accuracy of solution, and applies to any system of differential equations with derivatives continuous or piecewise continuous with finite jumps. ILLIAC library subroutine #F7, University of Illinois Digital Computer Laboratory, is a digital computer program applying this method.