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

Using the simple case of the Blasius similarity solution, we illustrate a recently developed general method (Costin et al 2012 Nonlinearity 25 125-64; Costin et al 2012 arXiv: 1209.1009) 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 the contraction mapping theorem in a suitable space of functions provides the existence of the 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 a finite domain.