A higher order uniform convergence result for a turning point problem
Turning point problems of the form \(-\varepsilon u''- xa(x) u'+ b(x)u= f(x)\) with boundary conditions \(u(-1)= u(1)= 0\) are considered. Replacing the functions \(a(x)\), \(b(x)\) and \(f(x)\) by piecewise polynomials of degree \(k\), an iterative process is proposed which yields a \(k\)th order approximation to the solution, uniformly in \(\varepsilon> 0\). For the convergence proof a new stability estimate is developed.
scientific article; zbMATH DE number 509983