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Solving a System of Nonlinear Equations
In this example we generate and verify a C program that solves a system of nonlinear equations.

Minimization of Free Energy
Here we consider steady-state heat conduction on a three-dimensional domain. The solution of the same physical problem can be obtained via multiple methods, shown here as a minimum of the free energy of the system. The domain of the example is a cube filled with water and containing a constant heat source. The upper surface is isolated so that there is no heat flow over the boundary. On all other sides a constant temperature is maintained. The task is to calculate the temperature distribution inside the cube.