AbstractIn this paper a straightforward derivation of one‐ and two‐dimensional finite difference forms for general cartesian networks is given. General analytic compact expressions up to third order for first derivatives are specifically derived. General cartesian networks with locally telescoping subnetworks are also introduced and the basic problem of approximating derivative boundary conditions is clarified. The applicability of these general finite difference forms is shown by solving numerically the Laplace problem with mixed Dirichlet–Neumann boundary conditions for an elliptic d