# how to solve the Blasius problem using gegenbauer in maple?

The steady, laminar, incompressible, viscous flow over a semi-infinite flat plate can be expressed by the following boundary value problem

${\partial u \over\partial x}+{\partial v\over\partial y}=0$

$u{\partial u \over\partial x}+v{\partial v\over\partial y}=v{\partial^2 u\over\partial y^2}$

with boundary conditions:

$u(x,0)=v(x,0)=0 ,u(x,\infty)=U_\infty$

Here, $u$ and $v$ are the velocity components along the flow direction ($x$-direction) and normal to the flow direction ($y$-direction), $v$ is the kinematic viscosity and $U_\infty$ is a constant free stream velocity.

how can I develope this in maple using gegenbauer function?

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This is a year late, and you may already know about it, but for reference, there is a recent article titled Solving a laminar boundary layer equation with rational Gegenbauer functions (see http://www.sciencedirect.com/science/article/pii/S0307904X12001242, may unfortunately be behind a paywall) which solves the Blasius problem using a collocation method where the collocation functions are rational Gegenbauer functions.

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