Numerical methods for the primitive equations (PEs) of oceanic flow are presented in this paper. First, a two-dimensional Poisson equation with a suitable boundary condition is derived to solve the surface pressure. Consequently, we derive a new formulation of the PEs in which the surface pressure Poisson equation replaces the nonlocal incompressibility constraint, which is known to be inconven...

This paper formulates and analyzes a weak solution to the coupling of time-dependent Navier-Stokes flow with Darcy flow under certain boundary conditions, one of them being the Beaver-Joseph-Saffman law on the interface. Existence and a priori estimates for the weak solution are shown under additional regularity assumptions. We introduce a fully discrete scheme with the unknowns being the Navie...

In this paper, we give a fourth-order compact finite difference scheme for the general forms of two point boundary value problems and two dimensional elliptic partial differential equations (PDE’s). By decomposing the coefficient matrix into a sum of several matrixes after we discretize the original problem, we can obtain a lower bound for the smallest eigenvalue of the coefficient matrix. Thus...

In this work, radial basis function collocation method (RBFCM) is implemented for generalized time fractional Gardner equation (GTFGE). The RBFCM meshless and easy-to-implement in complex geometries higher dimensions, therefore, it highly demanding. the Caputo derivative of order ? (0, 1] used to approximate first whereas, Crank-Nicolson scheme hired space derivatives. numerical solutions are p...

In this study, we will construct numerical techniques for tackling the logarithmic Schrödinger’s nonlinear equation utilizing explicit scheme and Crank-Nicolson of finite difference method. These schemes be subjected to accuracy stability tests before being used. Efficacy robustness under consideration demonstrated using an exact solution, one-Gausson, as well conserved quantities. Interaction ...