Invariant imbedding applied to homogeneous two-point boundary-value problems with a singularity of the first kind

摘要

It is shown that previous work of Elder can be used to extend the version of invariant imbedding due to M. R. Scott to homogeneous (vector) differential systems having a singularity of the first kind. The boundary conditions considered consist of existence (finite) at the singularity and specified values for some subset of the dependent variables at a second point. The important special case of a second-order equation is discussed in some detail. Computational considerations are discussed and numerical examples are presented.