This work presents the construction and implementation of a two-parameter exponentially fitted Taylor method suitable for solving ordinary differential equations that possess oscillatory or periodic behaviour. The methodology is based on six-step algorithm discussed in literature. We present associated truncation error demonstrate its accuracy using two test cases. gave better results compared ...

BACKGROUND This paper addresses the problem of detecting sleep spindles and K-complexes in human sleep EEG. Sleep spindles and K-complexes aid in classifying stage 2 NREM human sleep. NEW METHOD We propose a non-linear model for the EEG, consisting of a transient, low-frequency, and an oscillatory component. The transient component captures the non-oscillatory transients in the EEG. The oscil...

The paper is concerned with the discretization and solution of DAEs of index 1 and subject to a highly oscillatory forcing term. Separate asymptotic expansions in inverse powers of the oscillatory parameter are constructed to approximate the differential and algebraic variables of the DAEs. The series are truncated to enable practical implementation. Numerical experiments are provided to illust...

introduction: studying long-term trend changes of meteorological parameters is one of the routine methods in atmospheric studies, especially in the climate change subject. among the meteorological parameters, temperature is always considered as one of the most atmospheric elements and studying it in order to gain a better understanding of the climate change phenomenon, has been effective. in ad...

We present a new third-order essentially non-oscillatory central scheme for approximating solutions of twodimensional hyperbolic conservation laws. Our scheme is based on a two-dimensional extension of the centered weighted essentially non-oscillatory (CWENO) reconstruction we presented in Levy et al. [3]. This is a “true” 2D method; it is not based on a direction-by-direction approach. Our met...

A cross between the asymptotic expansion of an oscillatory integral and the Filon-type methods is obtained by applying a Filon-type method on the error term in the asymptotic expansion, which is in itself an oscillatory integral. The efficiency of the approach is investigated through analysis and numerical experiments, and a potential for better methods than current ones is revealed. In particu...