A comparative study of invariant imbedding and superposition

Abstract

A comparison is made between a certain version of invariant imbedding and the method of superposition, as represented by the Goodman-Lance method of complementary functions, with regard to their computational efficiency and effectiveness for linear two-point boundary-value problems. The comparison is most complete for the class of problems termed normal. For such problems superposition appears to be preferable for problems with a sufficiently short underlying interval, on grounds of lesser effort, but the accuracy of super position degenerates more rapidly than that of invariant imbedding as the interval length increases, and consequently the latter method seems preferable for long problems. General areas of possible future investigation are identified.

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