High Accuracy Iterative Solution of Convection Diffusion Equation with Boundary Layers on Nonuniform Grids

Fourth‐order compact schemes of a heat conduction problem with Neumann boundary conditions

“…The substitutions into (10) of (11)(12)(13)(14), and afterward simplifications give the following result:…”

Fourth‐order compact schemes for solving multidimensional heat problems with Neumann boundary conditions

“…From the above derivation, it can be seen that the new set of schemes, (4)- (13), has a truncation error of order t 2 + h 4 in time and space, and hence, it is consistent with the original differential equations.…”

“…What makes these two sets of schemes different from many others, such as those reported in [2] and [3][4][5][6][7][8][9][10][11][12][13][14], is that they are uniformly fourth-order at both interior and boundary points. The LOD method is used so that the schemes are constructed through a sequence of two or three one-dimensional equations.…”

Accuracy, robustness and efficiency comparison in iterative computation of convection diffusion equation with boundary layers

“…It was used as a test problem for FCS on nonuniform grids by Gupta et al for 0.01 ≤ ≤ 1 [7], and by us for 10 −8 ≤ ≤ 1 [12]. The coefficients of the convective terms are constant.…”

“…Recently, this scheme has been extended to nonuniform grids [7,11]. We used it with a multigrid method in [12] and obtained good results for some test problems with large Re.…”