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In this paper, we obtain some new Lyapunov-type inequalities for a class of even-order linear differential equations, the results are new and generalize and improve some early results in this field. [ABSTRACT FROM AUTHOR]

A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from three problems that were posed in symbolic form. Two problems are TIMSS items (a linear inequality and an equation involving square roots). The other problem involves square roots. We found that the majority of student pairs used symbol manipulation when solving the problems, and while many students seemed to prefer symbolic over graphical and tabular representations in their first attempt at solving the problems, we found that it was common for student pairs to use more than one strategy throughout the course of their solving. Students `use of graphing calculators to solve the problems is discussed. [ABSTRACT FROM AUTHOR]

In this paper we discuss some linear algebra issues concerning the implementation of blended implicit methods (J. Comput. Appl. Math. 2000; 116:41–62, Appl. Numer. Math. 2002; 42:29–45, J. Comput. Appl. Math. 2004; 164–165:145–158, In Recent Trends in Numerical Analysis, Trigiante D (ed.), Nova Science Publication Inc.: New York, 2001; 81–105) for the numerical solution of ODEs. In particular, we describe the strategies, used in the numerical code BiM (J. Comput. Appl. Math. 2004; 164–165:145–158), for deciding whether re-evaluating the Jacobian and/or the factorization involved in the non-linear splitting for solving the discrete problem. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we define the polyadic Pavelka algebras as algebraic structures for Rational Pavelka predicate calculus (RPL∀). We prove two representation theorems which are the algebraic counterpart of the completness theorem for RPL∀. [ABSTRACT FROM AUTHOR]

We consider meshless collocation methods for the numerical solution of transport processes described by hyperbolic conservation laws. The future goal is the construction of a robust and reliable meshfree discretization method for the equations of gas dynamics in complex geometries. In this paper we start with the simplest scalar model problems and analyze basic problems occurring in the grid-free approach. A topological condition on clouds of points is derived and several possible versions of a generalized Lax-Friedrichs scheme are discussed with respect to their numerical dissipation. A moving least-squares approach is followed to construct a positive discretization for solutions with shocks which is thoroughly analyzed and applied to test problems. [ABSTRACT FROM AUTHOR]

The paper presents a combined fine-coarse mesh TLM method. This technique reduces the memory storage and the computational time when modelling complex structures. In the combined fine-coarse mesh model, the region of interest is covered with a set of transmission-line fine meshes. The remaining part is covered with regular (or irregular) coarse meshes. The fine-mesh nodes are connected through busbars to the adjacent coarse-mesh nodes. The combined fine-coarse mesh TLM technique is applied to some diffusion problems. Significant savings in computational time and memory storage are obtained without loss of accuracy. [ABSTRACT FROM AUTHOR]

The boundary residual method is a powerful technique for solving EM boundary-value problems. This technique produces matrices difficult to solve using many of the standard numerical techniques. This paper discusses lesser-known numerical aspects of this method, and it shows efficient and well-conditioned methods to solve both the homogeneous' and non-homogeneous boundary residual problem. [ABSTRACT FROM AUTHOR]