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...

This paper describes a method of generating high order difference approxith matians to an m — order differential operator L using (m + 1) pointsIt uses certain auxiliary points for each (m + 1)-tuple in order to achieve an arbitrary specified order of truncation error in the difference approximation. In the context of solving Lu = f, this method may be interpreted as using L^u = I^f where is an...

In this paper, a kind of Fast Multipole Boundary Element Method (FM-BEM) based on series form expansion is presented to solve two-dimensional (2-D) Helmholtz equation problems. A theorem of multipole expansion is derived and proved for the fundamental solution, which demonstrates the error source and can be widely used in 2-D electromagnetics and acoustics problems. The truncation error is anal...

We give an error estimate for the Energy and Helicity Preserving Scheme (EHPS) in second order finite difference setting on axisymmetric incompressible flows with swirling velocity. This is accomplished by a weighted energy estimate, along with careful and nonstandard local truncation error analysis near the geometric singularity and a far field decay estimate for the stream function. A key ing...

In area efficient low error compensation multiplier design is using fixed width RPR(Reduced Precision Redundancy). We propose a new method called fixed width RPR for DSP applications. This fixed width multiplier is placed in ANT architecture to meet high speed, low power consumption and area efficiency. The fixed RPR is designed with compensation circuit for minimizing the occurrence of error. ...

This paper discusses an approach to evaluating accuracy of numerical integration in simulation of linear electrical network transients. Both modes of the free motion of a linear network (i.e. modes of the general solution of the differential equations) and modes of the forced motion (particular solution) are distorted independently when numerical integration is performed. The distortions of the...

In area efficient low error compensation multiplier design is using fixed width RPR (Reduced Precision Redundancy). We propose a new method called fixed width RPR for DSP applications. This fixed width multiplier is placed in ANT architecture to meet high speed, low power consumption and area efficiency. The fixed RPR is designed with compensation circuit for minimizing the occurrence of error....

The numerical solution of a linear singularly-perturbed reaction-diffusion two-point boundary value problem is considered. The method used is adaptive movement of a fixed number of mesh points by equidistribution of a user-chosen monitor function. A partly heuristic argument based on truncation error analysis leads to several suitable monitor functions, but also shows that the standard arc-leng...

This article is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave equations. A three-level second-order implicit algorithm is considered without introducing auxiliary variables. As a perturbation of the algorithm, a locally one-dimensional (LOD) procedure which has a splitting error not larger than the truncation error is suggested to solve problems...

We examine stability of summation by parts (SBP) numerical schemes that use hyperboloidal slices to include future null infinity in the computational domain. This inclusion serves mitigate outer boundary effects and, future, will help reduce systematic errors gravitational waveform extraction. also study a setup with truncation error matching. Our SBP-Stable scheme guarantees energy balance for...