Third and fourth order Taylor–Galerkin schemes have shown to be efficient finite element schemes for the numerical simulation of time-dependent convective transport problems. By contrast, the application of higher-order Taylor–Galerkin schemes to mixed problems describing transient transport by both convection and diffusion appears to be much more difficult. In this paper we develop two new Tay...

Interval Taylor methods for the validated solution of initial value problems for ODEs were introduced by Moore (1965a, 1965b, 1966). Lohner (1987, 1988, 1992) developed a comprehensive software package of an advanced interval Taylor method, which he applied successfully to many linear and nonlinear problems. But, as Lohner (1988) remarked, the step size of his method is limited by the step size...

A recent series of breakthroughs initiated by Spielman and Teng culminated in the construction of nearly linear time Laplacian solvers, approximating the solution of a linear system Lx = b, where L is the normalized Laplacian of an undirected graph. In this paper we study the space complexity of the problem. Surprisingly we are able to show a probabilistic, logspace algorithm solving the proble...

This paper suggests a new method discretization of nonlinear system using Taylor series expansion and zero-order hold assumption. This method is applied into the sampled-data representation of a nonlinear system with input time delay. Additionally, the delayed input is time varying and its amplitude is bounded. The maximum time-delayed input is assumed to be two sampling periods. Them mathemati...

An overview of the background of Taylor series methods and the utilization of the differential algebraic structure is given, and various associated techniques are reviewed. The conventional Taylor methods are extended to allow for a rigorous treatment of bounds for the remainder of the expansion in a similarly universal way. Utilizing differential algebraic and functional analytic arguments on ...

A treecode algorithm is presented for evaluating electrostatic potentials in a charged particle system undergoing screened Coulomb interactions in 3D. The method uses a farfield Taylor expansion in Cartesian coordinates to compute particle–cluster interactions. The Taylor coefficients are evaluated using new recurrence relations which permit efficient computation of high order approximations. T...

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Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opin...