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1. Variation of parameters and solutions of composite products of linear differential equations

Author

Littlejohn, Lance L. and López, José L.

Subjects
*VARIATIONAL principles, *NUMERICAL solutions to linear differential equations, *GREEN'S functions, *HOMOGENEOUS spaces, *SPECIAL functions, *LEGENDRE'S functions
Abstract

Abstract: Given a basis of solutions to k ordinary linear differential equations , we show how Green''s functions can be used to construct a basis of solutions to the homogeneous differential equation , where ℓ is the composite product . The construction of these solutions is elementary and classical. In particular, we consider the special case when . Remarkably, in this case, if is a basis of , then our method produces a basis of for any . We illustrate our results with several classical differential equations and their special function solutions. [Copyright &y& Elsevier]

Published
2010
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