Temperature Profile in a Rectangular Plate

Solves finite difference equations to get temperature profile in rectangular plate.

The method uses finite differences to solve Laplace equation and matrix inversion to solve the resulting system of linear algebraic equations. The rectangular plate has both dimensions set equal to unity. Each dimension is discretized and the total number of nodal points is equal to 29*29. To solve the system AU=X where U is the unknown temperatures at the interior nodal points, we must write the equations and find out X and A. Construction of vector X is done using boundary conditions: temperature in all sides is zero except in one side where it is equal to 100*sin(Pi*y).