On the use of asymptotically motivated gauge functions to obtain convergent series solutions to nonlinear ODEs

@article{Naghshineh2022OnTU,
  title={On the use of asymptotically motivated gauge functions to obtain convergent series solutions to nonlinear ODEs},
  author={Nastaran Naghshineh and Wolfgang Reinberger and Nathaniel S. Barlow and Mohamed A. Samaha and Steven J. Weinstein},
  journal={IMA Journal of Applied Mathematics},
  year={2022}
}
We examine the power series solutions of two classical nonlinear ordinary differential equations of fluid mechanics that are mathematically related by their large-distance asymptotic behaviors in semi-infinite domains. The first problem is that of the “Sakiadis” boundary layer over a moving flat wall, for which no exact analytic solution has been put forward. The second problem is that of a static air–liquid meniscus with surface tension that intersects a flat wall at a given contact angle… 

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References

SHOWING 1-10 OF 33 REFERENCES

The Blasius Function in the Complex Plane

This work calculates several numerical constants, such as the second derivative of f at the origin and the two parameters of the linear asymptotic approximation to f, to at least eleven digits and derives an expansion in rational Chebyshev functions TL j which converges exponentially fast with the truncation.

An Introduction to Fluid Dynamics

Keywords: dynamique des : fluides Reference Record created on 2005-11-18, modified on 2016-08-08

Free surface shapes in rigid body rotation: Exact solutions, asymptotics and approximants

This work analyzes steady interface shapes in zero gravity in rotating right circular cylindrical containers under rigid body rotation and applies the method of asymptotic approximants to yield analytical expressions for the height of the meniscus and the length of a spinning bubble over the whole range of rotation speeds.

Accurate closed-form solution of the SIR epidemic model

Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation

We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., Q. J. Mech. Appl. Math. 70 (2017) 21–48.) yields accurate analytic

Numerical Comparisons of Blasius and Sakiadis Flows

Momentum laminar boundary layers of an incompressible fluid either about a moving plate in a quiescent ambient fluid (Sakiadis flow) and the flow induced over a resting flat-plate by a uniform free

Advanced mathematical methods for scientists and engineers I: asymptotic methods and perturbation theory.

Eventually, you will enormously discover a supplementary experience and execution by Spending more cash by spending more cash.

Pade´ approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain

We describe a four-step algorithm for solving ordinary differential equation nonlinear boundary-value problems on infinite or semi-infinite intervals. The first step is to compute high-order Taylor