This paper studies a central difference and quartic spline approximation based exponential time differencing Crank-Nicolson (ETD-CN) method for solving systems of one-dimensional nonlinear Schrödinger equations and twodimensional nonlinear Schrödinger equations. A local extrapolation is employed to achieve a fourth order accuracy in time. The numerical method is proven to be highly efficient an...

In this workwe propose and analyze a fully discretemodifiedCrank–Nicolson finite element (CNFE)method with quadrature for solving semilinear second-order hyperbolic initial-boundary value problems. We prove optimal-order convergence in both time and space for the quadrature-modified CNFE scheme that does not require nonlinear algebraic solvers. Finally, we demonstrate numerically the order of c...

This project work report provides a full solution of simplified Navier Stokes equations for The Incompressible Couette Problem. The well known analytical solution to the problem of incompressible couette is compared with a numerical solution. In that paper, I will provide a full solution with simple C code instead of MatLab or Fortran codes, which are known. For discrete problem formulation, im...

We consider a linear, Schrödinger type p.d.e., the ‘Parabolic’ Equation of underwater acoustics, in a layer of water bounded below by a rigid bottom of variable topography. Using a change of depth variable technique we transform the problem into one with horizontal bottom, for which we establish an a priori H estimate and prove an optimal-order error bound in the maximum norm for a Crank-Nicols...

The temperature distribution due to a rotating or dithering Gaussian laser beam on a finite body is obtained numerically. The authors apply various techniques to solve the nonhomogeneous heat equation in different spatial dimensions. The authors’ approach includes the Crank-Nicolson method, the Fast Fourier Transform (FFT) method and the commercial software COMSOL. It is found that the maximum ...