An Assessment of Numerical Software for Solving Two-Point Boundary-Value Problems Arising in Heat Transfer

Abstract

The use of robust general-purpose user-oriented software packages for solving systems of two-point boundary-value problems for ordinary differential equations (BVODEs) is considered for the solution of BVODEs that commonly arise in the modeling of problems in heat transfer. This investigation involves three packages, DVCPR, COLSYS, and DTPTB, which implement the trapezoidal rule with deferred corrections, the method of spline collocation at Gaussian points, and multiple shooting, respectively. The effectiveness of the packages is demonstrated by examining their performance on a variety of BVODEs that have appeared in the literature. In several cases the packages produce results quite different from published results, and since the packages are consistently in agreement with each other, questions must be raised about the validity of the latter. The packages are also used to treat B VODEs that were impossible to solve using techniques presented in the literature. The software packages DVCPR, COLSYS, and DTP...