
12-26 Mathematical Methods
boundary conditions may be one of the following
three types:
1. Dirichlet problem ( First boundary value problem)
The solution is prescribed along the boundary.
2. Neumann problem ( Second boundary value problem)
The derivative of the solution is prescribed along
the boundary.
3. Mixed problem ( Third boundary value problem)
The solution and its derivative are prescribed
along the boundary.
Any of the above conditions is called homo geneous
if it is a zero-condition and nonhomogeneous if it is
a nonzero condition.
12.13.4 Solution of One-dimensional
Heat Equation (or diffusion
equation)
Consider a long and thin wire, rod or ...