Single cell discretizations of order two and four for self-adjoint elliptic equations

摘要

Finite-difference schemes for the self-adjoint elliptic partial differential equation in two dimensions are developed. The methods use either five or nine grid points of a single square cell of size 2h and have a truncation error of order h2 or h4. The resulting system of equations can be solved by iterative methods. Numerical results of two test problems with known analytical solutions are appended.