We present an unconditionally stable second-order hybrid numerical method for solving the Allen–Cahn equation representing amodel for antiphase domain coarsening in a binary mixture. The proposed method is based on operator splitting techniques. The Allen–Cahn equation was divided into a linear and a nonlinear equation. First, the linear equation was discretized using a Crank–Nicolson scheme an...

In this paper, a three-stage fourth-order numerical scheme is proposed. The first and second stages of the proposed are explicit, whereas third stage implicit. A compact considered to discretize space-involved terms. stability in space time checked using von Neumann criterion for scalar case. region obtained by more than one given explicit Runge–Kutta methods. convergence conditions found syste...

mistreated (Isenberg-Grezda, Kutberg & Nicolson, 2012, Isenberg-Grezda; Chabon & Nicolson, 2014). There is a need for translational research in this field to connect “bench to bedside” in order to find the best ways to help patients with ARBD. Public health managers should take responsibility of such a relevant issue, as many of these patients are at the boundaries of different medical speciali...

In this paper we transfer the a priori error analysis for the discretization of parabolic optimal control problems on domains allowing for H regularity (i.e. either with smooth boundary or polygonal and convex) to a large class of nonsmooth domains. We show that a combination of two ingredients for the optimal convergence rates with respect to the spatial and the temporal discretization is requ...

This paper proposes a numerical method to obtain an approximation solution for the time-fractional Schrödinger Equation (TFSE) based on combination of cubic trigonometric B-spline collocation and Crank-Nicolson scheme. The fractional derivative operator is described in Caputo sense. L1−approximation used discretization. Using Von Neumann stability analysis, proposed technique shown be condition...

The two-dimensional Burgers’ equation is a mathematical model to describe various kinds of phenomena such as turbulence and viscous fluid. In this paper, Crank-Nicolson finite-difference method is used to handle such problem. The proposed scheme forms a system of nonlinear algebraic difference equations to be solved at each time step. To linearize the non-linear system of equations, Newton’s me...

Solution of the diffusion equation is usually performed with the finite element discretization for the spatial elliptic part of the equation and the time dependency is integrated via some difference scheme, often the trapezoidal rule (Crank-Nicolson) or the unconditionally stable semi-implicit two-step algorithm of Lees. A common procedure is to use Picard’s iteration with the trapezoidal rule....

The numerical solution for a class of sub-diffusion equations involving a parameter in the range −1 < α < 0 is studied. For the time discretization, we use an implicit finite-difference Crank–Nicolson method and show that the error is of order k2+α , where k denotes the maximum time step. A nonuniform time step is employed to compensate for the singular behaviour of the exact solution at t = 0....