A finite difference scheme for the two?dimensional, second?order, nonlinear elliptic equation is developed. The difference scheme is derived using the local solution of the differential equation. A 13?point stencil on a uniform mesh of size h is used to derive the finite difference scheme, which has a truncation error of order h4. Well?known iterative methods can be employed to solve the resulting system of equations. Numerical results are presented to demonstrate the fourth?order convergence of the scheme. © 1995 John Wiley & Sons, Inc. Copyright © 1995 Wiley Periodicals, Inc.
| dc.contributor.author | Saldanha, G. | |
| dc.contributor.author | Ananthakrishnaiah, U. | |
| dc.date.accessioned | 2026-02-05T11:00:35Z | |
| dc.date.issued | A fourth?order finite difference scheme for two?dimensional nonlinear elliptic partial differential equations | |
| dc.description.abstract | 1995 | |
| dc.identifier.citation | Numerical Methods for Partial Differential Equations, 1995, 11, 1, pp. 33-40 | |
| dc.identifier.issn | 0749159X | |
| dc.identifier.uri | https://doi.org/10.1002/num.1690110104 | |
| dc.identifier.uri | https://idr.nitk.ac.in/handle/123456789/28070 | |
| dc.title | A finite difference scheme for the two?dimensional, second?order, nonlinear elliptic equation is developed. The difference scheme is derived using the local solution of the differential equation. A 13?point stencil on a uniform mesh of size h is used to derive the finite difference scheme, which has a truncation error of order h4. Well?known iterative methods can be employed to solve the resulting system of equations. Numerical results are presented to demonstrate the fourth?order convergence of the scheme. © 1995 John Wiley & Sons, Inc. Copyright © 1995 Wiley Periodicals, Inc. |