Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 20 of 22 for “"Runge-kutta methods."”.
-
Stability and efficiency properties of implicit Runge-Kutta methods
… certain stability properties of implicit Runge-Kutta methods. In particular, a new stability property is defined, which is a modification to non-autonomous problems of A-stability, and its relation to B-stability is considered. A Runge-Kutta method is written as [see 01front.pdf for …
-
The analysis and implementation of exponential almost Runge-Kutta methods for semilinear problems
… the multi-step Exponential Time Differencing Methods and the multi-stage Exponential Runge-Kutta Methods. A broader framework of Exponential General Linear Methods builds on these two families. We extend the classical Almost Runge-Kutta Method family, of multi-stage multi-value schemes, into …
-
Multimethods for the Efficient Solution of Multiscale Differential Equations
… Advances in computing hardware and numerical methods have allowed these models to become larger and more sophisticated. Increasingly, problems can be described as multiphysics and multiscale as they combine several different physical processes with different characteristics. If just one part …
-
Speeding up high-order algorithms in computational fluid and kinetic dynamics: based on characteristics tracing and low-rank structures
… challenges. First, classical discretization methods suffer from the curse of dimensionality, that is, the computational cost grows exponentially as the number of dimensions increases. Second, shock formations and sharp gradient structures that develop in certain PDEs of interest are …
-
Método gráfico para establecer el campo de pendientes de una Ecuación Diferencial
… diferencial. Presenta los métodos de Euler, Runge-Kutta de cuarto orden y el método multipasos de Adams-Bashforth-Moulton. Asimismo, se explica las ecuaciones mediante el uso del software para los métodos gráficos tales como el Maple y Geogebra. ABSTRACT: Oriented work in the area of …
-
Difference Methods for Stiff Delay Differential Equations
… significant in a dynamic process. Difference methods for approximating the solutions of stiff delay systems require special stability properties that are generalizations of those employed for stiff ordinary differential equations. Using the model equation (y'(t) = py(t) + qy(t-1), with complex …
-
Scalable High-Resolution Simulation of the Prey-Predator Model, with a Non-Local Consumption of Prey
… larger time steps compared to stability-limited Runge-Kutta methods. Benchmarking KSS against LEJA interpolation and Adaptive Krylov-Projection (AKP) exponential integrators on grids up to N = 8000 shows it maintains a constant iteration count of four Fast fourier tranforms (FFTs) per iteration, …
-
A Patankar Predictor-Corrector Approach for Positivity-Preserving Time Integration
… conservation laws. Standard time integration methods, including classical Runge-Kutta schemes, can violate these structural properties, leading to non-physical solutions. This thesis presents a novel positivity-preserving correction strategy applicable to general time integration schemes, with …
-
A Nondimensional Scaling Parameter for Predicting Pressure Wave Reflection in Stented Arteries
… Weighted Essentially Non-Oscillatory (WENO) and Runge-Kutta methods. Over 100 cases were tested. Results showed that reasonable variations in these parameters could induce changes in reflection magnitude of up to ±50%. It was also discovered that the relationship between each of these properties …
-
Analysis, simulation and design of nonlinear RF circuits
… are proposed. Both single- and multi-step methods are introduced. A large part of this section of the research is concerned with the application of Filon-type integration techniques to circuits subject to modulated signals. Such methods are tested with analog and digital modulated signals …
-
Relativistic neutron stars in general relativity and fourth order gravity
… we deal with stiffness by employing an IMEX Runge-Kutta scheme as opposed to the more computationally intensive fully implicit schemes or other adaptive Runge Kutta methods that may be impractical for partial differential equations. The first problem is focused on the mass-radius relation of …
-
Discontinuous Galerkin solutions of the Boltzmann equation: spectral collocation and moment methods
… the Boltzmann equation. Constructing numerical methods for this equation is a challenge, due in part to the kinetic theory description of moving particles, which relies on space, time, and velocity variables. Two novel approaches are presented and compared. The first uses a spectral collocation …
-
A multidomain spectral method for computational aeroacoustics
… do not involve the element corners. A set of Runge-Kutta methods optimized for wave propagation and with minimal storage requirements are developed for integration in time. Several radiation boundary conditions are implemented and tested, and a way to construct the spectral grids within the …
-
Advanced Time Integration Methods with Applications to Simulation, Inverse Problems, and Uncertainty Quantification
… We extend exponential propagation iterative methods of Runge-Kutta type (EPIRK) by [Tokman, JCP 2011], to build EPIRK-W and EPIRK-K time integration methods that admit approximate Jacobians in the matrix-exponential like operations. EPIRK-W methods extend the W-method theory by [Steihaug and …
-
Application of numerical methods to dislocation modeling of creep
… Dual-order, error-estimating, adaptive stepsize Runge-Kutta methods of Verner and of Fehlberg are used to solve the systems of ODE's. Predictions for the behavior of the stress exponent as a function of stress and model geometric parameters differ from predictions obtained using original models. …
-
SARK: a type-insensitive Runge-Kutta code
A novel solution method based on Mono-implicit Runge-Kutta methods has been fully developed and analysed for the numerical solution of stiff systems of ordinary differential equations (ODE). These Backward Runge-Kutta (BRK) methods have very desirable stability properties which make them efficient …
-
From efficient high-order methods to scientific machine learning.
… some limitations of the current Finite Element Methods (FEM) packages. We focus on the efficient implementation of implicit time discretization schemes, achieving computational savings by exploiting the structure of serendipity elements and developing a wrapper that integrates Machine Learning …
-
From efficient high-order methods to scientific machine learning.
… some limitations of the current Finite Element Methods (FEM) packages. We focus on the efficient implementation of implicit time discretization schemes, achieving computational savings by exploiting the structure of serendipity elements and developing a wrapper that integrates Machine Learning …
-
Solar radiation pressure, drag and gravitational effects on a dust particle in Earth orbit
… integrators or variational integrators (over the Runge-Kutta methods used here) may improve accuracy.
-
Problems in cosmology and numerical relativity
… with the robustness and accuracy of higher order methods. To this end, different modifications of the standard Berger-Oliger adaptive mesh refinement a logarithm have been proposed. In this work we present a new fourth order convergent mesh refinement scheme with sub- cycling in time for numerical …
Page 1 of 2