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arXiv · 1311.0421

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

O. Costin·T. Kim·S. Tanveer
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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.

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O. Costin, T. Kim, S. Tanveer. 2013-11-03. A quasi-solution approach to nonlinear problems - the case of Blasius similarity solution. https://doi.org/10.1088/0169-5983%2F46%2F3%2F031419

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