Abstract. The problem of non-local nonlinear non-Fickian polymer diffusion as modelled by a diffusion equation with a nonlinearly coupled boundary value problem for a viscoelastic ‘pseudostress’ is considered (see, for example, DA Edwards in Z. angew. Math. Phys., 52, 2001, pp. 254—288). We present two numerical schemes using the implicit Euler method and also the Crank-Nicolson method. Each sc...

We present a novel monolithic divergence-conforming HDG scheme for linear fluid-structure interaction problem with thick structure. A pressure-robust optimal energy-norm estimate is obtained the semidiscrete scheme. When combined Crank--Nicolson time discretization, our fully discrete energy stable and produces an exactly divergence-free fluid velocity approximation. The resulting system, which...

*Correspondence: [email protected] 2School of Science, Jiangnan University, Lihu Road, Wuxi, 214122, China Full list of author information is available at the end of the article Abstract In the study of pattern formation in bi-stable systems, the extended Fisher-Kolmogorov (EFK) equation plays an important role. In this paper, a Fourier pseudo-spectral method for solving the EFK equation in ...

An unconditionally stable finite difference scheme for systems whose dynamics are described by a fourth-order partial differential equation is developed with the use of a regular hexagonal grid. The scheme is motivated by the well-known Crank-Nicolson discretization that was originally developed for second-order systems and it is used to develop a discrete in time and space model of a deformabl...

A linear dispersive mechanism for error focusing in polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. ¿From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity. Several popular schemes are analyzed and are shown ...

Two discrete-time orthogonal spline collocation schemes are formulated and analyzed for solving the linear time-dependent Schrr odinger equation in two space variables. These are Crank-Nicolson and alternating direction implicit (ADI) schemes employing C 1 piecewise polynomial spaces of arbitrary degree 3 in each space variable. The stability of the schemes is examined and optimal order a prior...

In this work, we derive a goal-oriented a posteriori error estimator for the error due to time-discretization of nonlinear parabolic partial differential equations by the fractional step theta method. This time-stepping scheme is assembled by three steps of the general theta method, that also unifies simple schemes like forward and backward Euler as well as the Crank–Nicolson method. Further, b...