A New Third Order Exponentially Fitted Discretization for the Solution of Non-Linear Two Point Boundary Value Problems on a Graded Mesh

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

“…A new bi-cubic spline collocation method of fourth order accuracy has been designed by Singh and Singh [57] for a linear EPDE with DBCs. Most recently, new high accuracy approximations in exponential form for solving two-point BVPs on a variable mesh, and 2D nonlinear EPDEs on an unequal uniform mesh have been reported in [51] , [52] , [53] , [54] , [55] . Mohanty and Kumar [56] , and Priyadarshini and Mohanty [ 47 , 49 ] have proposed new high accuracy numerical algorithms for 2D quasilinear EPDEs using unequal mesh.…”

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

“…HOC FDMs in exponential form have been recently developed by Mohanty et al. [ 48 , 49 , 53 , 54 ] and Manchanda et al. [55] .…”

“…In order to obtain higher order approximations for and , let where , 1,2,3,4 are parameters to be evaluated. Using the approximations (40) , (43) , (46) – (52) , in ( 53 ), ( 54 ), we get where …”

A compact high resolution semi-variable mesh exponential finite difference method for non-linear boundary value problems of elliptic nature

“…To get more accurate results we need to devise a compact finite difference method of higher accuracy. Mohanty et al designed an exponential scheme of high accuracy using geometric mesh, employing off and full step discretization [12,13].…”