High precision compact numerical approximation in exponential form for the system of 2D quasilinear elliptic BVPs on a discrete irrational region.

This article presents a new approximation of order four in exponential form for two-dimensional (2D) quasilinear partial differential equation (PDE) of elliptic form with solution domain being irrational. It is further extended for application to a system of quasilinear elliptic PDEs with Dirichlet boundary conditions (DBCs). The main highlights of the method framed in this article are as under:•It uses a 9-point stencil with unequal mesh to approach the solution. The error analysis is discussed to authenticate the order of convergence of the proposed numerical approximation.•Various validating problems, for instance the Burgers' equation, Poisson equation in cylindrical coordinates, Navier-Stokes (NS) equations in rectangular and cylindrical coordinates are solved using the proposed techniques to depict their stability. The proposed approximation produces solution free of oscillations for large values of Reynolds Number in the vicinity of a singularity.•The results of the proposed method are superior in comparison to the existing methods of [49] and [56].