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Abstract: In this paper, a new definition of the filled function is given, it is different from the primary definition which was given by Ge in paper [R.P. Ge, A filled function method for finding a global minimzer of a function of several variables, Math. Program. 46 (1990) 191–204]. Based on the definition, a new filled function is proposed, and it has better properties. An algorithm for unconstrained global optimization is developed from the new filled function. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. [Copyright &y& Elsevier]

Abstract: Particle swarm optimization (PSO) as an efficient and powerful problem-solving strategy has been widely used, but appropriate adjustment of its parameters usually requires a lot of time and labor. So a co-evolving framework is proposed to improve the robustness of the PSO. In this paper, within this framework the fuzzy rules for the manipulation of the inertia weights are co-evolved with the particles. And the simulation results on a suite of test functions show that the use of this co-evolving framework improves the performance of the PSO, especially the robustness against the dimensional variation of the test functions. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematical analysis and computer algebra, a reliable algorithm of finite difference method for solving singular perturbation problems was established, a new matlab procedure ehssp was implemented, too. Several linear and non-linear problems are presented to illustrate the implementation of the program. [Copyright &y& Elsevier]

Abstract: A pyramid structure is a collection of connected mesh structures. It is well known that a pyramid structure of size n has a diameter of log n, which immediately leads to a natural routing algorithm, using only links between adjacent meshes. However, such paths are often unavailable because of the existence of faulty nodes and/or links. In this paper, we present the concept and technical details of an alternative routing algorithm, based on a collection of bypassing paths, for the potentially faulty pyramid structures that makes use of the links both within and between meshes contained in such structures. We also study some of the mathematical properties of this set of bypassing paths, including their average lengths, to suggest a characterization of the proposed alternative routing algorithm. [Copyright &y& Elsevier]

Abstract: Solving nonlinear equations is a problem often needed to be dealt with in the practical engineering application. This paper discusses preconditioning methods based on Block Broyden method. It first introduces the Block Broyden method and preconditioning technique. Then it presents four different preconditioners for the Block Broyden method and discusses the implementation process. It also analyzes the time complexity of the four algorithms. Finally, it solves the nonlinear systems arising from the Bratu problem by the four preconditioning algorithms. Experimental results show that the preconditioning technique is effective for the Block Broyden method and that the preconditioner SSOR has the fastest solving speed and the best performance among the four preconditioners. Therefore, it can be used in the large-scale problems arising from scientific and engineering computing. [Copyright &y& Elsevier]

Abstract: In this paper, for the nonlinear diffusion model of image denoising and segmentation, we present two high-order explicit algorithms and a semi-implicit algorithm using algebraic multi-grid method. The unconditional stability of the semi-implicit approximation is given. The numerical results of the above three algorithms are demonstrated with comparison to general explicit algorithm in [Y. Chen, B.C. Vemuri, L. Wang, Image denoising and segmentation via nonlinear diffusion, Comput. Math. Appl. 39 (2000) 131–149] for real noised images. The numerical results show that the implicit algorithm is quicker and sharper than all explicit algorithms. [Copyright &y& Elsevier]

Abstract: In this paper we introduce a reliable symbolic implementation of the algorithm for calculating Adomian polynomials and present some examples to show the simplicity and efficiency of the new method. [Copyright &y& Elsevier]

Abstract: Consider the problem of computing the smallest enclosing ball of a set of m balls in . This problem arises in many applications such as location analysis, military operations, and pattern recognition, etc. In this paper, we reformulate this problem as an unconstrained convex optimization problem involving the maximum function max{0, t}, and then develop a simple algorithm particularly suitable for problems in high dimensions. This algorithm could efficiently handle problems of dimension n up to 10,000 under a moderately large m, as well as problems of dimension m up to 10,000 under a moderately large n. Numerical results are given to show the efficiency of algorithm. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematics analysis and computer algebra, a reliable algorithm for solving high-order nonlinear Volterra–Fredholm integro-differential equations was established, and a new Maple procedure voltfredproc was established too. The results of the examples indicated that the procedure voltfredproc of Taylor polynomial method is simple and effective, and could provide an accuracy approximate solution or exact solution of the high-order nonlinear Volterra–Fredholm integro-differential equation. This would be useful for solving integro-differential equation, integral equations and ordinary differential equation. [Copyright &y& Elsevier]