Recent trends on Computational and Mathematical Methods in Science and Engineering (CMMSE)

Computational Mathematics is in the edge of many branches of Science and Technology, as they develop as far it is involved. There exists a close relationship between the need of solving real problems arising from different areas as Physics, Chemistry, Engineering, Biomedicine or Economics, among others, and the mathematical modelization and approximation of the problems posed. This is the importance of the existence of meetings in which this interdisciplinary exchange of information is possible, as it happens at International Conference of Computational and Mathematical Methods in Science and Engineering (CMMSE). This Conference has shown to be an effective melting pot of scientific knowledge from different branches of academic and industrial world. We have the pleasure to present some selectedmanuscripts from those exposed at the Computational andMathematical Methods in Science and Engineering (CMMSE) Conference. This Special Issue continues a fruitful line of CMMSE special issues (see [1–4]). The algorithmic characterization of the nonsingular almost strictly sign regular matrices bymeans of Neville elimination is the aim of the first paper of this volume, by P. Alonso et al. [5]. T. Goessens et al., in [6], propose a new three scale approach for textile models: a one-dimensional fiber model, a meso-level in the middle and a fabric model. The authors present two upscaling techniques for the three step multiscale model, based on the application of the volume averaging method on a non-linear diffusion equation at the first level and an overlapping domain decomposition. In [7], M. Grimmonprez et al. investigate the problem of nonlinear parabolic integro-differential equations with a known Neumann boundary condition on a part of the boundary and an unknown Dirichlet boundary condition on the other part of the boundary, as well as its approximation by means of a numerical time-discrete scheme. The authors in Real dynamics for damped Newtons method applied to cubic polynomials [8], analyze the real dynamics of the damped Newtons methods applied to cubic polynomials, finding different behaviors to be avoided such as convergence to n-cycles or even chaos. A block matrix analysis is proposed in Some results on determinants and inverses of nonsingular pentadiagonal matrices [9], to justify and modify a known algorithm for computing the determinant of a nonsingular pentadiagonal matrix having nonzero entries on its second subdiagonal, improving its accuracy and efficiency. The design of analytical theories of planetary motion is addressed by J.A. López et al. in [10] by means of Poisson series developments depending on the selection of the anomaly to be used. In thiswork the authors develop an improved algorithm in order to use arbitrary anomalies included in the class of generalized Sundman anomalies as temporal variables. The paper Error estimates for the full discretization of a nonlocal parabolic model for type-I superconductors [11], states an estimation of the solution of a vectorial nonlocal linear parabolic problem in terms of themagnetic field for superconductors of type-I. The convergence of the scheme and the corresponding error estimates are derived under appropriate assumptions. The efficient estimation of the solutions of nonlinear systems of equations is the aim of the research presented by J.L. Hueso et al. in [12]. In this work the authors present a new family of iterative methods and its generalization, getting a new family with order of convergence six. Real dynamics is used to compare its performance with already known iterative schemes. The authors in Low-complexity root-finding iteration functionswith no derivatives of any order of convergence [13], propose a procedure to design Steffensen-type iterative methods, optimal in the sense of Kung–Traub’s conjecture. The main advance of this procedure is that the schemes are transformed from iterative ones that use the derivatives, holding the order of convergence and the complexity introduced in the methods is minimum.