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Fourth‐order finite difference method for three‐dimensional elliptic equations with nonlinear first‐derivative terms
Author(s) -
Jain M. K.,
Jain R. K.,
Mohanty R. K.
Publication year - 1992
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690080606
Subject(s) - mathematics , diagonal , mathematical analysis , order (exchange) , nonlinear system , convergence (economics) , derivative (finance) , finite difference , dirichlet boundary condition , finite difference method , dirichlet distribution , dirichlet problem , second derivative , elliptic curve , boundary value problem , geometry , physics , finance , quantum mechanics , financial economics , economics , economic growth
We present a 19‐point fourth‐order finite difference method for the nonlinear second‐order system of three‐dimensional elliptic equations Au xx + Bu yy + Cu zz = f , where A , B , C , are M × M diagonal matrices, on a cubic region R subject to the Dirichlet boundary conditions u ( x , y , z ) = u (0) ( x , y , z ) on ∂ R . We establish, under appropriate conditions, O ( h 4 ) convergence of the difference method. Numerical examples are given to illustrate the method and its fourth‐order convergence. © 1992 John Wiley & Sons, Inc.