In-Class Example: A Simple Grid

Let’s create a class to represent a structured grid that we can use to represent data for solving PDEs via finite-difference methods.

We want our grid class to store:

• The domain limits, xmin, and xmax

• The number of points in the discretization, nx

• The coordinate vector, x

• A solution vector, phi

We can then write functions to:

• Output the solution to the screen or file (as x[i] phi[i] in columns)

• Compute the norm of a vector on our grid, e.g., the L2 norm:

  \[\|e\|_2 = \left ( \Delta x \sum_i | e_i | {}^2 \right )^{1/2} \]