We have been given a program that can solve the following equation using finite difference methods:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]- \epsilon \left( \frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} \right) - \frac{\partial \phi}{\partial x} = \sin \left(\pi y\right) \quad x,y \, \in \, (0,1)[/tex]

This is a convection diffusion model of ocean currents where the x-direction is east and the y-direction is north. And [itex]\phi = 0[/itex] on the boundaries.

I’ve managed to do most the problems for this but we asked to investigate the case when the Earth is rotating in the opposite direction, by changing the sign of the convection term. However I am unsure what that term is. Also I’m a little dodgy on my finite difference methods for partial differential equations, how exactly do they differ from working out finite difference methods for ordinary differential equations?

Any help at all will be greatly appreciated.

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# Finite difference methods

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