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 ...

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...

This paper deals with the numerical solution of a class of reaction diffusion equations arises from ecological phenomena. When two species are introduced into unoccupied habitat, they can spread across the environment as two travelling waves with the wave of the faster reproducer moving ahead of the slower.The mathematical modelling of invasions of species in more complex settings that include ...

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...

In this paper, a discrete singular convolution (DSC) algorithm is introduced to solve Fisher’s equation, to which obtaining an accurate and reliable traveling wave solution is a challenging numerical problem. Two novel numerical treatments, a moving frame scheme and a new asymptotic scheme, are designed to overcome the subtle difficulties involved in the numerical solution of Fisher’s equation....

Flow movement in unsaturated soil can be expressed by a partial differential equation, named Richards equation. The objective of this study is the finding of an appropriate implicit numerical solution for head based Richards equation. Some of the well known finite difference schemes (fully implicit, Crank Nicolson and Runge-Kutta) have been utilized in this study. In addition, the effects of di...

In this paper, we propose third-order semi-discretized schemes in space based on the tempered weighted and shifted Grunwald difference (tempered-WSGD) operators for fractional diffusion equation. We also show stability convergence analysis fully discrete scheme a Crank–Nicolson time. A Black–Scholes equation is proposed tested numerically. Some numerical experiments are carried out to confirm a...

This article concerns the numerical approximation of two-dimensional nonstationary Navier–Stokes equations with $$H^1$$ initial data. By utilizing special locally refined temporal stepsizes, we prove that linearly extrapolated Crank–Nicolson scheme, usual stabilized Taylor–Hood finite element method in space, can achieve second-order convergence time and space. Numerical examples are provided t...

We develop and demonstrate a computationally efficient numerical splitting technique for solving the reaction–diffusion equation. The scheme is based on the Strang splitting technique wherein the portions of the governing equations containing stiff chemical reaction terms are separated from those parts containing the less-stiff transport terms. As demonstrated, the scheme achieves second-order ...