Transformed Hermite functions on a finite interval and their applications to a class of singular boundary value problems
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In this paper, a weighted orthogonal system on finite interval based on the transformed Hermite functions is introduced. Some results on approximations using the Hermite functions on finite interval are obtained from corresponding approximations on infinite interval via a conformal map. To illustrate the potential of the new basis, we apply it to the collocation method for solving a class of singular two-point boundary value problems. The numerical results show that our new scheme is very effective and convenient for solving singular boundary value problems.
KeywordsTransformed Hermite functions Collocation Conformal map Singular boundary value problems
Mathematics Subject ClassificationPrimary 65L60 Secondary 34B16
The authors are grateful to the reviewers for carefully reading this paper and for their comments and suggestions which have improved the paper.
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