Construction of additive semi-implicit Runge-Kutta methods with low-storage requirements

The final publication is available at Springer via http://dx.doi.org/ 10.1007/s10915-015-0116-2Space discretization of some time-dependent partial differential equations gives rise to systems of ordinary differential equations in additive form whose terms have different stiffness properties. In these cases, implicit methods should be used to integrate the stiff terms while efficient explicit methods can be used for the non-stiff part of the problem. However, for systems with a large number of equations, memory storage requirement is also an important issue. When the high dimension of the problem compromises the computer memory capacity, it is important to incorporate low memory usage to some other properties of the scheme. In this paper we consider Additive Semi-Implicit Runge-Kutta (ASIRK) methods, a class of implicitexplicit Runge-Kutta methods for additive differential systems. We construct two second order 3-stage ASIRK schemes with low-storage requirements. Having in mind problems with stiffness parameters, besides accuracy and stability properties, we also impose stiff accuracy conditions. The numerical experiments done show the advantages of the new methods.Supported by Ministerio de Economía y Competividad, project MTM2011-23203

Numerical positivity for Runge-Kutta methods

Over the last years, a great effort has been done to develop Runge-Kutta methods preserving qualitative properties of the exact solution like monotonicity of positivity.Some results are available in the literature that ensure these properties under certain stepsize restictions. However, these results are given for the exact numerical solution whereas in practice the numerical solution available is only an approximation of it. For example, when implicit Runge-Kutta methods are used, the numerical solution obtained comes out from the inexact numerical resolution of nonlinear systems. The aim of this work is the study of the effective stepsize restrictions for positivity when implicit Runge-Kutta schemes are used. To achive this goal, we consider separately the problem of finding positive stage value predictors, and the analysis of the iterative scheme used, in this case Newton method

Una mirada matemática por Sevilla. El parque María Luisa

El papel que ha jugado y que juega la Educación en nuestras vidas es fundamental, forma a la sociedad con el fin de generar una colectividad unida, colaborativa, cooperante, inteligente y capacitada. Al mismo tiempo que la sociedad crece y avanza, la educación debe progresar y que sirva para alentar, abordar posibles problemas que presente en este caso la juventud, incentivar y motivar al alumnado. De esta manera, se deben reformular, aplicar o estudiar nuevas metodologías de aprendizaje, que aspiren a ser un aprendizaje significativo, en la que el estudiante es capaz de asociar la información nueva obtenida con la que ya posee, construyendo así su propio conocimiento. Por eso mismo, el presente Trabajo Fin de Máster, persigue mediante la aplicación de nuevas metodologías, la elaboración de una actividad innovadora y con ayuda de la realidad que nos rodea (la arquitectura, el urbanismo, la historia, el arte y la cultura) conseguir afianzar y construir conocimientos, en este caso específicamente de matemáticas. Y que a su vez, consiga motivar al alumnado, llevando las matemáticas a la cotidianidad. En esta ocasión, la realidad más cercana es la ciudad de Sevilla, con lo cual, se convierte en el escenario perfecto para poder desarrollar dicha actividad innovadora. Existen espacios como El Alcázar de Sevilla, donde ya se viene conjugando Matemáticas y Arquitectura desde hace tiempo. Sin embargo, ante tal Bien Inmueble y teniendo en cuenta su debida protección y conservación, realizar diferentes actividades con el alumnado en dicho espacio, se convierte en una tarea complicada. Por eso mismo, se selecciona El Parque de María Luisa, como escenario idóneo para poder realizar diferentes actividades con el alumnado de Secundaria, donde las Matemáticas, la Historia, el Arte y la Arquitectura, e incluso otras asignaturas, se fusionen y sean capaces de desarrollar y construir conocimiento.The role that education has played and plays nowadays in our lives is essential, it educates society in order to create an united, cooperative, intelligent and prepared community. Education must progress that society grows and moves forward, and it must also serve to encourage students, deal with the problems presented by youth people and stimulate the whole student body. New methodologies that aim for being a meaningful learning in which the students are able to associate new information with the information that they already know, thus producing their own knowledge, must be reformulated, applied and studied. This is the reason why, this post – graduate final project intends to elaborate an innovative activity by means of the implementation of new methodologies and the reality that surrounds us (Architecture, Urban planning, History, Art and culture). This project also looks for consolidating and creating knowledge, especially in Maths. And at the same time it wants to encourage the student body by bringing Maths to everyday nature. This time, the closest reality is Seville, therefore it becomes the perfect stage for the development of this innovative activity. There are some places such as the ‘Alcázar de Sevilla’ where Maths and Architecture were joined long time ago. However, carrying out educational activities with students there is an arduous task because the monument is an immovable property which involves its due protection and conservation. This is the reason why the Maria Luisa Park has been chosen like the perfect setting in order to carry out different activities with students from secondary school in which Maths, History, Art, Architecture and even other subjects are fused and are able to develop and produce knowledge.Universidad de Sevilla. Máster en Profesorado de Enseñanza Secundaria Obligatoria y Bachillerato, Formación Profesional y Enseñanzas de Idioma

Cardiopatía estructural en pacientes anticoagulados con fibrilación auricular no valvular: prevalencia y perfil clínico en una muestra nacional

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