# 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…

## 2 Citations

### On The Power Series Solution to The Nonlinear Pendulum

- Physics, MathematicsThe Quarterly Journal of Mechanics and Applied Mathematics
- 2022

The exact solution to the simple pendulum problem has long been known in terms of Jacobi elliptic functions, of which an efficient numerical evaluation is standard in most scientific computing…

### On the shape of an axisymmetric meniscus rising from a static liquid pool

- Mathematics
- 2022

. We examine the classical problem of the height of a static liquid interface that forms on the outside of a solid vertical cylinder in an unbounded stagnant pool exposed to air. Gravitational and…

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