It is with pleasure that we offer the readers of the International Journal of Computer Mathematics this special issue consisting of some of the most significant contributions to computational and mathematical methods with applications in science and engineering presented at the 11th International Conference of Computational and Mathematical Methods in Science and Engineering, CMMSE-2011, held at Alicante, Spain, 26–30 June 2011. This particular special issue is the last one to date in a series of special issues dating back to CMMSE-2002 Citation1 Citation15 Citation16,Citation19–24.
Since its inception in 2000, the International Conference of Computational and Mathematical Methods in Science and Engineering has been a multi-disciplinary conference, covering all numerical areas of science and engineering. The aim of the CMMSE is to encourage cross-fertilization between different disciplines and to gain new insights into the emerging developments in mathematical and computational methods. New developments will be required in order to examine the ever more complicated science and engineering problems arising in our society.
The first paper of this special issue, by Romaguera et al. Citation14, extends Schellekens’ method in order to yield asymptotic upper bounds for a certain class of recursive algorithms and improves the original Schellekens’ method by introducing a new fixed-point technique.
The article Dedekind–MacNeille completion and Cartesian product of multi-adjoint lattices, by Morcillo et al. Citation12, adapts the classical notion of Dedekind–MacNeille completion in order to relax some usual hypothesis on such ordered sets, and they study the advantages of generating multi-adjoint lattices as the Cartesian product of previous ones.
The third article, Key exchange protocols over noncommutative rings. The case of
Citation5, introduces some key exchange protocols over non-commutative rings, also gives a security analysis of the proposed protocols and concludes that the only possible attack is by brute force.
The research by Bianco et al. Citation3 considers a simple predator–prey system with two possible habitats and where an epidemic spreads by contact among the predators, in the patch in which prey are absent.
In their work, Application of the network method to simulate elastostatic problems defined by potential functions. Applications to axisymmetrical hollow bodies, Morales et al. Citation10 use the network method to make most of the potent computational algorithms implemented in electrical simulation codes and to allow an easy implementation of the complex boundary conditions inherent to this potential formulation in comparison with other classical numerical methods.
In New additional conditions for the numerical uniqueness of the Boussinesq and Timpe solutions of elasticity problems Citation11, the authors propose new additional simple conditions of Dirichlet type for the numerical uniqueness of the solution of elastostatic axisymmetric problems formulated in terms of the Boussinesq and Timpe potential functions, as particular cases of the Papkovich–Neuber representation.
The work Public parks management via mathematical tools Citation17 considers a mathematical model for the interaction of wild and domestic herbivores with a natural or man-maintained landscape.
Cordero et al. Citation7 analyse the dynamical behaviour of the operators associated with multi-point interpolation iterative methods and frozen derivative methods for solving nonlinear equations applied to second-degree complex polynomials.
In the article The convergence of a new symmetric iterative splitting method for non-autonomous systems, Tanoǧlu and Korkut Citation18 construct a new symmetric iterative splitting scheme based on the Magnus expansion for solving non-autonomous problems.
Solving systems of nonlinear equations is a very important task since the problems emerge mostly through the mathematical modelling of real problems. Self-adaptive combination of global tabu search and local search for nonlinear equations Citation13 shows that a self-adaptive combination of a metaheuristic with a classical local search method can converge for some difficult problems that are not solved by Newton-type methods.
In Finite semifields with 74 elements, by Combarro et al. Citation6, the authors present efficient computational techniques to classify four-dimensional finite semifields.
Combinatorial structures of three vertices and Lie algebras Citation4 shows a characterization of digraphs of three vertices associated with Lie algebras and determines the list of isomorphism classes for Lie algebras associated with these digraphs.
De Cos et al. Citation8 analyse the factors that have influence on the lead time of batches of metallic components of aerospace engines. In their article Solving anisotropic elliptic and parabolic equations by a meshless method: Simulation of the electrical conductivity of a tissue, Gavete et al. Citation9 give the extension of the generalized finite difference method to the solution of anisotropic elliptical and parabolic partial differential equations in the case of two space dimensions.
The research underlying the article by Ashyralyev and Hicdurmaz Citation2 considers schemes of the first and second orders of accuracy difference for the mixed problem for the multidimensional fractional Schrödinger differential equation with dependent coefficients.
Finally, we thank all the authors and referees for their excellent contributions to this special volume. We also express our gratitude to the Spanish Ministry of Education for grant MTM2011-13393-E.
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