A fourth order di_erence method for a nonlinear elliptic PDEs in two dimension space

Abstract EN

In this article, we have presented a novel high order di_erence method for solving nonlinear elliptic equations with constant coe_cients in two dimensions cartesian coordinate system subject to dirichlet boundary conditions.

the present fourth order method based on the exponential techniques.

the method reduces to central di_erence method when exponential function present in method linearized.

we present numerical experiments to demonstrate the e_ciency of the method and validity of our fourth order method.