Abstract
A method of analyzing and interpreting trajectory errors in the numerical solution of ordinary differential equations by digital computers is discussed. Truncation in integrating a set of differential equations leads to errors in the trajectory of the solution. An explanation is given for the use of diagrams in the complex plane to evaluate errors in the trajectory, with a discussion of the properties of a number of frequently used integration formulas via the diagrams. The diagrams portray the characteristics of an integration method in more detail than do the absolutely stable regions presented by Dahlquist. Based on the diagrams, guidelines are listed as to how to choose a proper integration formula for the given set of differential equations. A method is presented to check whether or not the numerical solution is satisfactory.
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