Single cell finite difference approximations ofO(kh2 +h4) for ?u/?x for one space dimensional nonlinear parabolic equation

On the use of AGE algorithm with a high accuracy Numerov type variable mesh discretization for 1D non-linear parabolic equations

“…Further, Mohanty and Khosla [6,7] have studied the application of alternating group explicit (AGE) iterative method, which is suitable for the use on parallel computers, for the solution of two point non-linear singular boundary value problems, on a non-uniform mesh. Using three spatial grid points, Mohanty et al [8] and [9] have developed new implicit two-level compact finite difference methods for the solution of spatially one dimensional non-linear parabolic equations. Later, Mohanty and Evans [10] have discussed the application of AGE algorithm to the method discussed in [8].…”

“…For σ l = 1 (constant mesh case), that is, for h l+1 = h l = h, the method (12) reduces to two level implicit difference method whose local truncation error is of O(k 2 + kh 2 + h 4 ) for the solution of the differential equation (1) (see, Mohanty et al [8]). …”

“…Using three spatial grid points, Mohanty et al [8] and [9] have developed new implicit two-level compact finite difference methods for the solution of spatially one dimensional non-linear parabolic equations. Later, Mohanty and Evans [10] have discussed the application of AGE algorithm to the method discussed in [8]. Recently, using three-spatial grid points Arora et al [11] and Mohanty [12] have derived two-level stable implicit variable mesh methods for the solution of initial boundary value problem (1)-(3).…”

Compact operator method of accuracy two in time and four in space for the numerical solution of coupled viscous Burgers’ equations

“…Dai and Chen [6] have developed a lower order conditionally stable explicit scheme for viscous Burgers' equation. Using uniform mesh discretization and 3-spatial grid-points, two-level implicit difference methods of order two in time ðtÞ and four in space ðxÞ for the solution of viscous Burgers' equation in one dependent variable were discussed in [7][8][9][10][11][12][13]. The coupled Burgers' equations belong to an important class of fluid flow equations.…”

Numerical solutions of one-dimensional non-linear parabolic equations using Sinc collocation method

“…They have considered Neumann boundary conditions for the solutions. Moreover, we can point to many other efficient methods for solving these problems, see [11][12][13][14][15][16][17].…”