Fourth‐order finite difference scheme for a system of quasilinear elliptic equations

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.