Singularly perturbed boundary value problems for a class of second order turning point on infinite interval
An asymptotic solution of the singularly perturbed boundary value problem \[ \begin{aligned} &\epsilon y''+x^2y'+\left(2x-\epsilon Px^2\right)y=0,\;x\in \mathbb R, \\ &y(\pm\infty),\;y(0+)=A,\;y(0-)=B, \end{aligned} \] with positive constants \(A,B\) and \(P\) is constructed. The analysis is based on using asymptotic expansion techniques and confluent hypergeometric functions. Finally, the accuracy of the approximation is discussed in detail.
scientific article; zbMATH DE number 6113026
scientific article