Higher order approximation in exponential form based on half-step grid-points for 2D quasilinear elliptic BVPs on a variant domain

This paper reports a new fourth order Finite Difference Method (FDM) in exponential form for two-dimensional quasilinear boundary value problem of elliptic type (BVPE) with variant solu-tion domain. Further, this discretization is extended to solve the system of quasilinear BVPEs. Following are the main highlights of the proposed FDM:center dot An unequal mesh 9-point compact stencil is used to approximate the solution. Half-step points are used to evaluate the known variables of this problem. The convergence theory is studied for unequal mesh to validate the fourth order convergence of the suggested FDM.center dot It is applicable to BVPE irrespective of coordinate systems. Various benchmark problems, for example, Poisson equation in cylindrical coordinates, Burgers' equation, Navier-Stokes (NS) equa-tions in cylindrical and rectangular coordinates, are solved to depict their fourth order conver-gence.center dot Numerical results confirm the accuracy, trustworthiness and acceptability of the suggested nu-merical algorithm. These results endorse the superiority of the proposed FDM over the previously existing techniques of Mohanty and Kumar (2014), Mohanty and Setia (2014), Priyadarshini and Mohanty (2021).