Preface
In this section, we show some problems of practical significance.
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Introduction to Linear Algebra with Mathematica
Glossary
Applications
Rayleigh problem
In fluid dynamics, Rayleigh problem also known as Stokes first problem is a problem of determining the flow created by a sudden movement of a plane from rest, named after Lord Rayleigh and Sir George Stokes. This is considered as one of the simplest unsteady problem that have exact solution for the Navier-Stokes equations.
Consider an infinitely long plate which suddenly made to move with constant velocity U in the x direction, which is located at y = 0 in an infinite domain of fluid, which is at rest initially everywhere. The incompressible Navier-Stokes equations reduce to
The problem on the whole is similar to the one dimensional heat conduction problem. Hence a self-similar variable can be introduced
In Mathematica, we plot a donat
Fisher equation
Consider the famous Fisher equation
- Rayleigh problemWikipedia
- Batchelor, George Keith. An introduction to fluid dynamics. Cambridge university press, 2000.
- Kudryashov, N.A., On one of methods for finding exact solutionsof nonlinear differential equations
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