The finite-difference time-domain (FDTD) method based on the iterated Crank–Nicolson (ICN) scheme is extended to a frequency-dependent version. Drude model used express metal dispersion, which incorporated into formulation with trapezoidal recursive convolution technique. validity of present convolutional perfectly matched layers discussed through analysis metal-insulator-metal plasmonic wavegu...

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...

This work proposes a numerical scheme for class of time-fractional convection–reaction–diffusion problems with time lag. Time-fractional derivative is considered in the Caputo sense. The comprises discretization technique given by Crank and Nicolson temporal direction spline functions tension factor are used spatial direction. Through von Neumann stability analysis, shown conditionally stable. ...

The Burgers equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank Nicholson, used for solving the one-dimensional Burgers equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to the conve...

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...