Collocation Software for Boundary-Value ODEs

The use of a general-purpose code, COLSYS, is described. The code is capable of solving mixed-order systems of boundary-value problems in ordinary differential equations. The method of spline collocation at Gaussian points is implemented using a B-spline basis. Approximate solutions are computed on a sequence of automatically selected meshes until a user-specified set of tolerances is satisfied. A damped Newton's method is used for the nonlinear iteration. The code has been found to be particularly effective for difficult problems. It is intended that a user be able to use COLSYS easily after reading its algorithm description. The use of the code is then illustrated by examples demonstrating its effectiveness and capabilities.

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