  Finite Difference (FD) schemes are widely used in science and engineering for
approximating solutions of partial differential equations (PDEs). Error
analysis of FD schemes relies on estimating the truncation error at each time
step. This approach usually leads to a global error whose order is of the same
order of the truncation error. For classical FD schemes the global error is
indeed of the same order as the truncation error. A particular class of FD
schemes is the Block Finite Difference (BFD) schemes, in which the grid is
divided into blocks. The structure of such schemes is similar to the structure
of the Discontinuous Galerkin (DG) method, and allows inhabitation of the
truncation errors. Recently, much effort was devoted to design BFD schemes
whose global error converges faster than the truncation error. In this paper,
we elaborate the approach presented in arXiv:1711.07926 for the heat equation
with periodic boundary conditions. We generalize this methodology to design BFD
schemes for the heat equation with Dirichlet or Neumann boundary conditions,
whose global error converges faster than the truncation error. Such schemes are
henceforth called Error Inhibiting Schemes. We provide an explicit error
analysis, including proofs of stability and convergence of the proposed
schemes. We illustrate our approach using several numerical examples, which
demonstrate the efficiency of our method in comparison to standard FD schemes.

Numerical Analysis;Numerical Analysis