RT info:eu-repo/semantics/doctoralThesis
T1 Rational methods without order reduction for abstract evolution problems
A1 Arranz Simón, Carlos
A2 Universidad de Valladolid. Escuela de Doctorado
K1 Ecuaciones en derivadas parciales
K1 Numerical analysis
K1 Análisis numérico
K1 Differential equations
K1 Ecuaciones diferenciales
K1 Rational methods
K1 Métodos racionales
K1 12 Matemáticas
AB Partial differential equations are fundamental tools for modeling the temporal evolution of a wide range of relevant phenomena in fields such as physics, ecology, and economics. Their use for practical purposes requires the numerical approximation of their solutions, which are generally difficult to obtain analytically. Runge–Kutta methods, widely employed for this purpose, exhibit a reduction in their order of convergence when applied to this type of equations. This phenomenon limits the accuracy and efficiency of numerical simulations, making it necessary to develop new strategies to overcome it. The objective of this document is the design, analysis, and implementation of temporal numerical integration schemes, based on the rational functions of these methods, that avoid this order reduction. These problems are formulated as abstract evolution equations within the framework of semigroup theory of operators, which allows them to be treated in a unified and quite general way. In this manner, the proposed rational methods are developed progressively, starting from linear problems and subsequently incorporating nonlinear terms and boundary conditions. They exhibit good convergence, stability, and efficiency properties, which open the door to their extension to more complex problems and to their application in realistic simulations.
YR 2025
FD 2025
LK https://uvadoc.uva.es/handle/10324/81858
UL https://uvadoc.uva.es/handle/10324/81858
LA spa
NO Escuela de Doctorado
DS UVaDOC
RD 20-ene-2026