A simple form for the fourth order difference method for 3-D elliptic equations

• Published in: Applied mathematics and computation Vol. 184; no. 2; pp. 589 - 598
• Main Authors: Dehghan, Mehdi, Molavi-Arabshahi, Seyedeh Mahboubeh
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.01.2007; Elsevier
• Subjects: Elliptic partial differential equations; Exact sciences and technology; Finite difference schemes; Fourth order technique; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Finite difference schemes; Fourth order technique; Elliptic partial differential equations; Transcendental equation; Three-dimensional calculations; Recurrence relation; Initial value problem; Boundary condition; Partial differential equation; Non linear equation; Numerical analysis; Elliptic equation; Boundary value problem; Applied mathematics; Finite difference method
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2006.05.156

In 1992, Jain et al. [M.K. Jain, R.K. Jain, R.K. Mohanty, Fourth-order finite difference method for three dimensional elliptic equations with nonlinear first-derivative terms, Numer. Meth. Part. Differ. Equat. 8 (1992) 575–591] proposed a fourth order finite difference scheme for the 3-D elliptic equation. In this paper, we present a simple and new form of 19-point fourth order difference method for the nonlinear second-order 3-D elliptic difference equation Au xx + Bu yy + Cu zz = f( x, y, z, u, u x , u y , u z ), where A, B and C are constants on a cubic region W subject to the Dirichlet boundary conditions on ∂ W.