Invariant imbedding, difference equations, and elliptic boundary value problems

✍ Scribed by Edward Angel

• Publisher: Elsevier Science
• Year: 1970
• Tongue: English
• Weight: 591 KB
• Volume: 4
• Category: Article
• ISSN: 0022-0000
• DOI: 10.1016/s0022-0000(70)80044-7

✦ Synopsis

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.