The objectives of the present study are to investigate thermal radiation of a viscous incompressible unsteady chemically reacting and hydromagnetic fluid flow past an impulsively started vertical plate with heat and mass transfer is analyzed. The fluid is a gray, absorbing-emitting but nonscattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy...

In the present investigation, the fully implicit and Crank–Nicolson difference schemes for solving option prices are analyzed. It is proved that the error expansions for the difference methods have the correct form for applying Richardson extrapolation to increase the order of accuracy of the approximations. The difference methods are applied to European, American, and down-and-out knock-out ca...

We present a generalization of the often-used Crank-Nicolson (CN) method of obtaining numerical solutions of the time-dependent Schrödinger equation. The generalization yields numerical solutions accurate to order (Deltax)2r-1 in space and (Deltat)2M in time for any positive integers r and M, while CN employ r=M=1. We note dramatic improvement in the attainable precision (circa ten or greater o...

In this paper, we study a numerical simulation method for the initial-boundary problem of dissipative of the generalized symmetric regularized long-wave equations with damping term. A nonlinear-implicit Crank-Nicolson finite difference scheme is constructed. The scheme is a twoleveled scheme. The error estimations, convergence, stablity and uniqueness of the solution are proven by discrete ener...

The semi-implicit leapfrog time-discretization is a workhorse algorithm for initial-value MHD codes to bridge between vastly separated time scales. Inclusion of atomic interactions with neutrals breaks the functional structure equations that exploited by leapfrog. We address how best integrate physics into Following Crank-Nicolson method, one approach time-center in linear solver and use Newton...

A semi-Lagrangian method is presented to price continuously observed fixed strike Asian options. At each timestep a set of one dimensional partial integral differential equations (PIDEs) is solved and the solution of each PIDE is updated using semi-Lagrangian timestepping. Crank-Nicolson and second order backward differencing timestepping schemes are studied. Monotonicity and stability results ...

This paper addresses the construction of absorbing boundary conditions for the one-dimensional Schrödinger equation with a general variable repulsive potential or with a cubic nonlinearity. Semi-discrete time schemes, based on Crank-Nicolson approximations, are built for the associated initial boundary value problems. Finally, some numerical simulations give a comparison of the various absorbin...

A semilinear second-order parabolic equation is considered in a regular and a singularly perturbed regime. For this equation, we give computable a posteriori error estimates in the maximum norm. Semidiscrete and fully discrete versions of the backward Euler, Crank–Nicolson, and discontinuous Galerkin dG(r) methods are addressed. For their full discretizations, we employ elliptic reconstructions...

This paper is concerned with transparent boundary conditions (TBCs) for wide angle “parabolic” equations (WAPEs) in underwater acoustics (assuming cylindrical symmetry). Existing discretizations of these TBCs introduce slight numerical reflections at this artificial boundary and also render the overall Crank–Nicolson finite difference method only conditionally stable. Here, a novel discrete TBC...

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...