THE EXPANSION POINT METHOD FOR IMPROVED CALCULATION OF DIFFICULT TRANSPORT INTEGRALS

Abstract

In a previous article, the authors introduced a new method for the improved asymptotic evaluation of Laplace integrals of the type for large x, where k must be 1 or 2 (Hanna and Davis, 2011). This method (called optimal exponential or OE) also applies to the acceleration of regular perturbation and power series. Here we develop a new analytical procedure (called expansion point or XP) to evaluate more general problems of the type . This includes the most general Watson lemma problem of the type , which cannot be handled by the OE method. The XP method is simple and general and offers good practical accuracy. It is especially powerful when combined with an “extended” exponential procedure. Application of the new method is illustrated with several problems important in chemical engineering.

Keywords:

• Asymptotics
• Expansion-point improvement
• Exponential improvement
• Integrals
• Power series
• Regular perturbations
• Watson's lemma

Acknowledgment

We appreciate the helpful suggestions of the three anonymous reviewers.

Notes

For k = β or k = 2β, the change of variable t ^k  = y gives a Type I problem. Fj denotes d ^j  F/du ^j (u = 0)/j!.