D. J. Evans’s research while affiliated with Loughborough University and other places

In this article, we propose new difference methods of order two and four using three grid points in a coupled manner for solving the one dimensional nonlinear biharmonic problems with specified boundary conditions at the end points. The resulting matrix system is solved by the block iterative methods on a parallel computer. Derivatives of the solution are obtained as a by-product of the methods. Numerical examples are provided to demonstrate the efficiency and accuracy of the methods on both sequential and parallel computations.

We report alternating group explicit (AGE) iteration method to solve the tri-diagonal linear system derived from a new finite difference discretization of sixth order accuracy of the two point singular boundary value problem u"+\frac{α}{r}u'=f(r), 0 < r < 1, α =1 and 2 subject to boundary conditions u(0)=A, u(1)=B, where A and B are finite constants. We also discuss Newton-AGE iteration method for the sixth order numerical solution of two point non-linear boundary value problem. The proof for the convergence of the AGE iteration method when the coefficient matrix is real and unsymmetric is discussed. Numerical results are presented to illustrate the proposed iterative methods.

New derivations of the UL factorizations of Töplitz matrices of banded and circulant form are considered. Since the matrix factors have a special structure, very efficient non-linear Gauss–Seidel and successive over-relaxation (SOR) methods can be obtained to solve the non-linear equations involved in deriving the U and L factors. Numerical evidence is presented which confirms the results and conclusions given.

The explicit methods although very suitable for parallel processing always deny us reasonable accuracy and some stability; on the other hand, the implicit schemes offer stability, but the exploitation of these methods for parallel processing may be difficult and possibly inefficient. The class of Group Explicit (GE) methods, introduced herein, is the sort of semi-explicit schemes which enable us with a trade-off between stability and the possibility of them being suitable for implementation of parallel systems. Furthermore, it is possible to express the semi-explicit schemes in terms of pure explicit formulae to enable their efficient implementation.

Association rule is one of the data mining techniques involved in discovering information that represents the association among data. Data in the database sometimes appear infrequent but highly associated with a specific data. This paper proposes a technique for significant rare data by introducing second support in discovering the association rules of such data. We show that the proposed approach provides better performance as compared to standard association rules techniques.

The determination of the diameter of an interconnection network is essential in evaluating the performance of the network. Parallelogramic honeycomb torus is an attractive alternative to classical torus network due to smaller vertex degree, and hence, lower implementation cost. In this paper, we present the expression for the diameter of a parallelogramic honeycomb torus, which extends a known result about rhombic honeycomb torus.

The well-known Simpson rule is an optimal two-step fourth-order method which is unconditionally unstable. In the present paper we describe a new L-stable version of the method. A suitable combination of the arithmetic average approximation with the explicit backward Euler formula provides a third-order approximation at the midpoint which, when plugged into the Simpson rule, gives a third-order L-stable scheme. The L-stable Simpson-type rule (LSIMP3) obtained is then employed to derive a third-order time integration scheme for the diffusion equation. Numerical illustrations are provided to compare the performance of the new LSIMP3 scheme with the Crank–Nicolson scheme. While the Crank–Nicolson scheme can produce unacceptable oscillations in the computed solution, the present LSIMP3 scheme can provide both stable and accurate approximations.

In this article, we analyze a linear feedback control algorithm particularly suited for the Available Bit Rate service class in an Asynchronous Transfer Mode (ATM) networks. We envisage the development of a closed-loop, fluid approximation model, in which the propagation delay is reflected across the network, while the rate of transmission and the queue occupancy are modeled as fluids. Using a fluid model has the advantage to permit a simplified study of the network behavior. The above model is described with the continuous-time system of delay-differential equations, which is solved semi-analytically. The contribution of this work is to provide a sending rate scheme, which is based on both a rate control function and a suitable fuzzy function for network load and delay. It is shown that the concept of fuzzy set theory can be proved beneficial in the analysis of network load and delay, whose uncertainty is an inherent characteristic. Finally, the developments in the area of time-delay systems control allow to compute exact stability bounds of the Round Trip Time (RTT) and thus to indicate if the connection is in a stable state.

In this paper, we present the interval version of the two parameter overrelaxation iterative (TOR) method and we obtain some convergence conditions when the matrix A of the linear system Ax = b belongs to some classes of matrice. Similar conditions were obtained for the point TOR method.Some results for the accelerated overrelaxation interval and point iterative (AOR) method were also obtained, which coincides with those given by Martins in Ref. [7].

In this paper, we propose a method of recovering shape from shading that solves directly for the surface height using neural networks. The main motivation of this paper is to provide an answer to the open problem proposed by Zhou and Chellappa [11]. We first formulate the shape from shading problem by combining a triangular element surface model with a linearized reflectance map. Then, we use a linear feed-forward network architecture with six layers to compute the surface height with a singular value decomposition. The weights in the model initialized using eigenvectors and eigen-values of the stiffness matrix of objective functional. Experimental results show that our solution is very effective.