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Fourth‐order finite difference scheme for a system of quasilinear elliptic equations
Author(s) -
Stys Tadeusz,
Stys Krystyna
Publication year - 1991
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.1690070206
Subject(s) - mathematics , mathematical analysis , boundary value problem , truncation error , discretization , algebraic equation , nonlinear system , physics , quantum mechanics
The system of two quasilinear elliptic equations is approximated by the method of lines, which has the truncation error O ( h 2 ) at points neighboring the boundary and O ( h 4 ) at the most interior points. It is proved that the global error of the method is O ( h 4 ) at all mesh points. The two‐point boundary value problem for the system of ordinary differential equations that arises from the method of lines is solved by the O ( h 4 ) convergent finite difference scheme, suitable to the equations of the form u xx = f ( x, u ) without the first derivative u x . The system of algebraic equations obtained by the full discretization is solved by Gauss elimination method for three diagonal matrices combined with the method of iterations. A numerical example is presented.