Fourth‐order finite difference method for three‐dimensional elliptic equations with nonlinear first‐derivative terms | Zendy

Jain M. K. | Zendy; Jain R. K. | Zendy; Mohanty R. K. | Zendy

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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.

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