A one-step 4-stage Hermite-Birkhoff-Taylor method of order 12, denoted by HBT(12)4, is constructed for solving nonstiff systems of first-order differential equations of the form y′ = f(x, y), y(x0) = y0. The method uses derivatives y′ to y(9) as in Taylor methods combined with a 4-stage Runge-Kutta method. Forcing an expansion of the numerical solution to agree with a Taylor expansion of the tr...

Implicit-explicit (IMEX) linear multistep time-discretization schemes for partial differential equations have proved useful in many applications. However, they tend to have undesirable time-step restrictions when applied to convection-diffusion problems, unless diffusion strongly dominates and an appropriate BDF-based scheme is selected (Ascher et al., 1995). In this paper, we develop Runge-Kut...

In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...

Abstract We consider solitary-wave solutions of the generalized Burger’s-Fisher equation ∂Ψ ∂t + αΨ δ ∂Ψ ∂x − ∂ 2Ψ ∂x2 = βΨ(1 − Ψδ). In this paper, we present a new method for solving of the generalized Burger’s-Fisher equation by using the collocation formula for calculating spectral differentiation matrix for Chebyshev-Gauss-Lobatto point. To reduce round-off error in spectral collocation met...

A family of predictor-corrector exponential Numerov-type methods is developed for the numerical integration of the one-dimensional Schrr odinger equation. The formula considered contains certain free parameters which allow it to be tted automatically to exponential functions. The new methods are very simple and integrate more exponential functions than both the well known fourth order Numerov t...

The efficiency of track reconstruction for particles detected in at least four stations is presented in Table 1. Two STS detector setups have been investigated. In the idealistic setup all stations are pixel-like detectors. The realistic setup consists of (going downstream) 2 MAPS detectors, 1 pixel detector and 4 double-sided silicon strip detectors with 15 stereo angle. Different number of pi...

To integrate large systems of locally coupled ordinary differential equations (ODEs) with disparate timescales, we present a multirate method with error control that is based on the Cash-Karp Runge-Kutta (RK) formula. The order of multirate methods often depends on interpolating certain solution components with a polynomial of sufficiently high degree. By using cubic interpolants and analyzing ...

Commencing from a global-error formula, originally due to Henrici, we investigate the accumulation of global error in the numerical solution of linear highly-oscillating systems of the form y 00 + g(t)y = 0, where g(t) t!1 ?! 1. Using WKB analysis we derive an explicit form of the global-error envelope for Runge{Kutta and Magnus methods. Our results are closely matched by numerical experiments....

In this paper, we use the spectral collocation method based on Chebyshev polynomials for spatial derivatives and fourth order Runge-Kutta (RK) method for time integration to solve the generalized Zakharov equation (GZE). Firstly, theory of application of Chebyshev spectral collocation method on the GZE is presented. This method yields a system of ordinary differential equations (ODEs). Secondly...