A quasi-solution approach to nonlinear problems - the case of Blasius similarity solution

Abstract

Using the simple case of Blasius similarity solution, we illustrate a recently developed general method that reduces a strongly nonlinear problem into a weakly nonlinear analysis. The basic idea is to find a quasi-solution $F_0$ that satisfies the nonlinear problem and boundary conditions to within small errors. Then, by decomposing the true solution $F=F_0+E$, a weakly nonlinear analysis of $E$, using contraction mapping theorem in a suitable space of functions provides the existence of solution as well as bounds on the error $E$. The quasi-solution construction relies on a combination of exponential asymptotics and standard orthogonal polynomial representations in finite domain.

arXiv admin note: substantial text overlap with arXiv:1303.1416