We analyze the spatially semidiscrete piecewise linear finite element method for a nonlocal parabolic equation resulting from thermistor problem. Our approach is based on the properties of the elliptic projection defined by the bilinear form associated with the variational formulation of the finite element method. We assume minimal regularity of the exact solution that yields optimal order erro...

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 address the problem of approximating numerically the solutions (Xt : t ∈ [0, T ]) of stochastic evolution equations on Hilbert spaces (h, 〈·, ·〉), with respect to Brownian motions, arising in the unraveling of backward quantum master equations. In particular, we study the computation of mean values of 〈Xt, AXt〉, where A is a linear operator. First, we introduce estimates on the behavior of X...

We develop a family of Eulerian-Lagrangian localized adjoint methods for the solution of the initial-boundary value problems for rst-order advection-reaction equations on general multi-dimensional domains. Diierent tracking algorithms, including the Euler and Runge-Kutta algorithms, are used. The derived schemes naturally incorporate innow boundary conditions into their formulations and do not ...

background: in this paper we compare a highly accurate supervised to an unsupervised technique that uses breast thermal images with the aim of assisting physicians in early detection of breast cancer. methods: first, we segmented the images and determined the region of interest. then, 23 features that included statistical, morphological, frequency domain, histogram and gray-level co-occurrence ...

The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both drift and diffusion coefficient are allowed grow super-linearly. existence uniqueness numerical solution generated by BEM proved convergence underlying one shown. Simulations provided illustrate theoretical results demonstrate application our in area system ...

Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyse fully discrete numerical method this geometric evolution equation. The uses piecewise linear finite elements in space and backward Euler approximation time. We establish existence uniqueness solution, as well an unconditional stability property. Some computations confirm the theoretical results demon...

We give a unified method to derive the strong convergence rate of backward Euler scheme for monotone SDEs in $L^p(\Omega)$-norm, with general $p \ge 4$. The results are applied SODEs polynomial growth coefficients. also generalize argument Galerkin-based SPDEs coefficients driven by multiplicative trace-class noise.

This is a continuation of the first author’s earlier paper [17] jointly with Pang and Deng, in which the authors established some sufficient conditions under which the Euler–Maruyama (EM) method can reproduce the almost sure exponential stability of the test hybrid SDEs. The key condition imposed in [17] is the global Lipschitz condition. However, we will show in this paper that without this gl...