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 contribution aims to propose a compact numerical scheme solve partial differential equations (PDEs) with q-spatial derivative terms. The is based on the q-Taylor series approach, and an operator proposed, which useful discretize second-order spatial q-derivative constructed using proposed operator, gives fourth-order accuracy for For time discretization, Crank–Nicolson, Runge–Kutta methods...

Abstract. We consider a partial differential equation of Schrödinger type, known as the ‘parabolic’ approximation to the Helmholtz equation in the theory of sound propagation in an underwater, rangeand depth-dependent environment with a variable bottom. We solve an associated initialand boundary-value problem by a finite difference scheme of Crank-Nicolson type on a variable mesh. We prove that...

Abstract. This article is devoted to the study of the finite element approximation for a nonlocal nonlinear parabolic problem. Using a linearised Crank-Nicolson Galerkin finite element method for a nonlinear reaction-diffusion equation, we establish the convergence and error bound for the fully discrete scheme. Moreover, important results on exponential decay and vanishing of the solutions in f...

A novel Exponential Time Differencing (ETD) Crank-Nicolson method is developed which is stable, second order convergent, and highly efficient. We prove stability and convergence for semilinear parabolic problems with smooth data. In the nonsmooth data case we employ a positivity-preserving initial damping scheme to recover the full rate of convergence. Numerical experiments are presented for a ...

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. ...