Boundary closure of a difference scheme
= Boundary closure of a difference scheme
A boundary closure supplies the boundary rows or ghost values needed by a spatial <finite difference method>. It must reflect the PDE boundary data and preserve a mesh-uniform stability estimate. Interior <Von Neumann stability analysis> cannot detect an arbitrary unstable boundary row; for example a row $U_1^{n+1}=2U_1^n$ produces growth even beside an otherwise stable heat stencil.