Solving PDEs

Here we show how the discretize package can be used to solve partial differential equations (PDE) numerically by employing the finite volume method. To solve a PDE numerically we must complete the following steps:

  1. Formulate the problem; e.g. the PDE and its boundary conditions
  2. Apply the weak formulation by taking the inner product of each PDE with a test function
  3. Formulate a discrete set of equations for the inner products according to the finite volume method
  4. Use the discrete set of equations to solve for the unknown variable numerically

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