Invariant imbedding, difference equations, and elliptic boundary value problems

摘要

This paper presents an invariant imbedding approach to the solution of coupled matrix-vector difference equations under two-point boundary conditions. It is shown that the finite difference approach to the solution of elliptic equations results in a special case of the coupled difference equations considered. For linear self-adjoint equations, the invariant imbedding approach yields stable initial value problems. Finally, the standard direct and iterative finite difference methods are derived and analyzed from the invariant imbedding equations.