Trueman.Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-domain method. IEEE Transactions on Microwave Theory and Techniques . 2006G. Sun,C. W. Trueman.Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-d...
The Crank–Nicolson difference method for the temporal and the weighted–shifted Grünwald–Letnikov difference method for the spatial discretization are proposed to achieve a second-order convergence in time and space. The D’Yakonov alternating–direction implicit technique, which is effective in two...
Runge–Kutta method; iterated Crank–Nicolson method; Wilson–Cowan equations; EEG simulation 1. Introduction In computational neuroscience, the Wilson–Cowan model is an important tool for studying neural activities in the brain [1,2,3]. It describes the interactions between excitatory and inhibitory...
(3) we approximate the derived coupled system with a fractional derivative with order α ∈ ( 0 , 1 ) by the modified L 1 Crank–Nicolson scheme with the developed new mixed element method; (4) we derive the stability of the new mixed element scheme and optimal error estimates in the ...
Runge–Kutta method; iterated Crank–Nicolson method; Wilson–Cowan equations; EEG simulation 1. Introduction In computational neuroscience, the Wilson–Cowan model is an important tool for studying neural activities in the brain [1,2,3]. It describes the interactions between excitatory and inhibitory...
By means of a proper orthogonal decomposition (POD) to cut down the dimensionality of unknown finite element (FE) solution coefficient vectors in the Crank–Nicolson (CN) mixed FE (CNMFE) method for two-dimensional (2D) unsteady Stokes equations in regard to vorticity stream functions, a reduce...
modified phase field crystal problem; Crank–Nicolson Leap-Frog; SAV method; second-order accuracy 1. Introduction It is well known that crystal phenomena (such as edge dislocation [1], deformation and plasticity in nanocrystalline materials [2], epitaxial growth, and zone refinement [3]) are ...
A weak singularity in the solution of time-fractional differential equations can degrade the accuracy of numerical methods when employing a uniform mesh, especially with schemes involving the Caputo derivative (order α,), where time accuracy is of the o