Fourth-order finite difference method for three-dimensional elliptic equations with nonlinear first-derivative terms

✍ Scribed by M. K. Jain; R. K. Jain; R. K. Mohanty

• Publisher: John Wiley and Sons
• Year: 1992
• Tongue: English
• Weight: 542 KB
• Volume: 8
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.1690080606

✦ Synopsis

We present a 19-point fourth-order finite difference method for the nonlinear second-order system of three-dimensional elliptic equations Au,, + Bu,, + Cu,, = f, where A, B, C, are M X M diagonal matrices, on a cubic region R subject to the Dirichlet boundary conditions u(x, y , z ) = U'~)(X,Y, z ) on aR. We establish, under appropriate conditions, O(h4) convergence of the difference method. Numerical examples are given to illustrate the method and its fourth-order convergence.