Two upwind finite difference schemes are considered for the numerical solution of a class of semilinear convection-diffusion problems with a small perturbation parameter ε and an attractive boundary turning point. We show that for both schemes the maximum nodal error is bounded by a special weighted `1-type norm of the truncation error. These results are used to establish ε-uniform pointwise co...

Noninvasive concentric ring electrodes are a promising alternative to conventional disc electrodes. Currently, the superiority of tripolar concentric ring electrodes over disc electrodes, in particular, in accuracy of Laplacian estimation, has been demonstrated in a range of applications. In our recent work, we have shown that accuracy of Laplacian estimation can be improved with multipolar con...

We present a uniformly accurate finite difference method and establish rigorously its uniform error bounds for the Zakharov system (ZS) with a dimensionless parameter 0 < ε ≤ 1, which is inversely proportional to the speed of sound. In the subsonic limit regime, i.e., 0 < ε 1, the solution propagates highly oscillatory waves and/or rapid outgoing initial layers due to the perturbation of the wa...

This work addresses a versatile modeling of complex photonic integrated circuits (PICs). We introduce a cosimulation solution for combining the efficient modeling capabilities of a circuit-level simulator, based on analytical models of PIC sub-elements and frequency-dependent scattering matrix (S-matrix) description, and an accurate electromagnetic field simulator that implements the finite ele...

Historically the finite volumemethods have been developed for the numerical integration of conservation laws. In this study we present some recent results on the application of such schemes to dispersive PDEs. Namely, we solve numerically a representative of Boussinesq type equations in view of important applications to the coastal hydrodynamics. Numerical results of the runup of a moderate wav...

A new third-order Energy Stable Weighted Essentially NonOscillatory (ESWENO) finite difference scheme for scalar and vector linear hyperbolic equations with piecewise continuous initial conditions is developed. The new scheme is proven to be stable in the energy norm for both continuous and discontinuous solutions. In contrast to the existing highresolution shock-capturing schemes, no assumptio...

We consider structure preserving numerical schemes for the Ostrovsky equation, which describes gravity waves under the influence of Coriolis force. This equation has two associated invariants: an energy function and the L norm. It is widely accepted that structure preserving methods such as invariants-preserving and multi-symplectic integrators generally yield qualitatively better numerical res...

We prove a regularity property of finite difference schemes for the heat or diffusion equation ut = ∆u in maximum norm with large time steps. For a class of time discretizations including L-stable single-step methods and the second-order backward difference formula, with the usual second-order Laplacian, we show that solutions of the scheme gain first spatial differences boundedly, and also sec...

in this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. we prove a posteriori $ l^2(l^2)$ and error estimates for this method under minimal regularity hypothesis. test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.

in this paper, based on the slab method of analysis, a novel and general approach isdeveloped for studying the radial forging process with curved profile dies. the presented approachis not only more general with respect to previous studies, but it is also easier to understand and useand can be efficiently used for optimization of the die profile depending on the forging geometryand conditions. ...