Elliptic1D

Solves the 1D Poisson equation with Robin boundary conditions.

\[ \nabla^2 u(x) = f(x) \]

with \(x\in[0,1]\), and \(f(x) =e^x\). The boundary conditions are given by

\[ au + b\frac{du}{dx} = g \]

with \(a=1\), \(b=1\), and \(g=0\), and

\[ au(0) + b\frac{du(0)}{dx} = 0 \]

\[ au(1) + b\frac{du(1)}{dx} = 2e \]

This corresponds to the call to robinBC1D of robinBC1D(k, m, dx, a, b).

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This example is implemented in:

• MATLAB/ OCTAVE

• C++

Additional MATLAB/ OCTAVE variants of this example with different boundary conditions:

• Homogeneous Dirichlet

• Non-Homogeneous Dirichlet

• Left Dirichlet, Right Neumann

• Left Dirichlet, Right Robin

• Left Neumann, Right Neumann

• Left Neumann, Right Robin

• Left Robin, Right Robin

• Periodic Boundary Conditions

• Non-Periodic Boundary Conditions