“…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.…”
“…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.…”
“…HOC FDMs in exponential form have been recently developed by Mohanty et al. [ 48 , 49 , 53 , 54 ] and Manchanda et al. [55] .…”
Section: Associated Research Work Done In the Pastmentioning
confidence: 99%
“…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 …”
“…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].…”
In this research an original exponential approximation of second accuracy in y- and third accuracy in x-axis employing full step discretization has been designed for solving 2D non-linear partial differential equation of elliptic nature in a rectangular domain. We adopted non-constant grid spacing in x -axis and constant grid spacing in y -axis in numerical computation of convection-diffusion equation where convection term dominates. An exhaustive error behaviour of the technique has been analysed. Non-linear elliptic equations are computed using this method. Lastly, proposed idea is scrutinized on simulations of physical repute with emphasis on convection-diffusion equation articulating the efficacy of the technique.
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