Abstract
An initial-value method, based on the use of certain compound matrices, is presented for the treatment of mathematically unstable two-point boundary-value problems. A distinctive feature of the method is that the solution is obtained from an auxiliary equation which is mathematically stable and it thereby avoids the well-known difficulties associated with, for example, the method of complementary functions. The method is described in detail for fourth-order equations but it is also shown how the method can easily be adapted to deal with second- and third-order equations.
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