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Grid refinement
Reliable PDE results require refinement studies, residual checks, and boundary-condition verification.
Stencil
A stencil approximates a differential operator from neighboring grid values.
PDE classes
Elliptic, parabolic, and hyperbolic PDEs demand different discretizations and stability diagnostics.
Heat equation
Parabolic schemes combine spatial discretization and time stepping; stability controls the time step.
CFL
CFL-type restrictions connect the time step with the spatial grid and propagation speed.
Poisson equation
Elliptic discretization typically gives a sparse linear system with boundary conditions built in.