A singularly perturbed delay parabolic problem of convection-diffusion type with a discontinuous convection coefficient and source term is examined. In the problem, strong interior layers weak boundary are exhibited due to large in spatial variable discontinuity source. The discretized by nonstandard finite difference scheme for time derivative, we used Crank–Nicolson scheme. To enhance order c...

Boundary value methods are applied to find transient solutions of M/M/2 queueing systems with two heterogeneous servers under a variant vacation policy. An iterative method is employed to solve the resulting large linear system and a Crank-Nicolson preconditioner is used to accelerate the convergence. Numerical results are presented to demonstrate the efficiency of the proposed method.

We present OpenMP version of a Fortran program for solving the Gross-Pitaevskii equation harmonically trapped three-component rotating spin-1 spinor Bose-Einstein condensate (BEC) in two spatial dimensions with or without spin-orbit (SO) and Rabi couplings. The uses either Rashba Dresselhaus SO coupling. use split-step Crank-Nicolson discretization scheme imaginary- real-time propagation to cal...

We describe the growth dynamics of a stock using stochastic differential equations with generalized logistic model which encompasses several well-known functions as special cases. For each model, we compute optimal variable effort policy and compare expected net present value total profit earned by harvester among policies. In addition, further extend study to include parameters sensitivity, su...

A full discrete stabilized finite element scheme for the transient Navier-Stokes equations is proposed, based on the pressure projection and the extrapolated trapezoidal rule. The transient Navier-Stokes equations are fully discretized by the lowest equal-order finite elements in space and the reduced Crank-Nicolson scheme in time. This scheme is stable for the equal-order combination of discre...

In two-phase incompressible flow problems surface tension effects often play a key role. Due to surface tension the pressure is discontinuous across the interface. In interface capturing methods the grids are typically not aligned to the interface and thus in problems with an evolving interface time dependent pressure spaces should be used. Hence, a method of lines approach is not very suitable...

We propose and analyze a novel, second-order in time, partitioned method for the interaction between an incompressible, viscous fluid and a thin, elastic structure. The proposed numerical method is based on the Crank–Nicolson discretization scheme, which is used to decouple the system into a fluid subproblem and a structure subproblem. The scheme is loosely coupled, and therefore at every time ...

We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin (IPDG) methods for solving nonlinear parabolic equations. Under some appropriate regularity conditions, we give the l(H) and l(L) error estimates of the fully discrete symmetric interior penalty discontinuous Galerkin (SIPG) scheme with the implicit θ-schemes in time...

EEcient numerical schemes for nonlinear diiusion ltering based on additive operator splitting (AOS) were introduced in 15]. AOS schemes are eecient and unconditionally stable, yet their accuracy is limited. Future applications of nonlinear diiusion ltering may require better accuracy at the expense of a relatively modest cost in computations and complexity. In this report we explore second orde...