Sökning: "Lie group method"

Visar resultat 1 - 5 av 22 avhandlingar innehållade orden Lie group method.

1. 1. Contributions to Numerical Solution of Stochastic Differential Equations

   Författare :Anders Muszta; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; adaptive method; change of time; CIR model; CKLS model; convergence order; Euler method; heavy-tailed SDE; hyperbolic SDE; geometric integration; global Lipschitz condition; Levy process; Lie group method; local Lipschitz condition; local martingales; mean reversion; Milstein method; numerical method; semimartingale; stochastic differential equation; stochastic Taylor expansion; strong approximation; symplectic integration; volatility induced stationarity; waveform relaxation; volatility induced stationarity;

   Sammanfattning : This thesis consists of four papers: Paper I is an overview of recent techniques in strong numerical solutions of stochastic differential equations, driven by Wiener processes, that have appeared the last then 10 years, or so. Paper II studies theoretical and numerical aspects of stochastic differential equations with so called volatility induced stationarity. LÄS MER

3. 2. Group classification of linear Schrödinger equations by the algebraic method

   Författare :Célestin Kurujyibwami; Peter Basarab-Horwath; Roman Popovych; Rita Tracinà; Linköpings universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

   Sammanfattning : This thesis is devoted to the group classification of linear Schrödinger equations. The study of Lie symmetries of such equations was initiated more than 40 years ago using the classical Lie infinitesimal method for specific types of real-valued potentials. LÄS MER

4. 3. Admissible transformations and the group classification of Schrödinger equations

   Författare :Celestin Kurujyibwami; Peter Basarab-Horwath; Roman Popovych; Pontelis Damianou; Linköpings universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES;

   Sammanfattning : We study admissible transformations and solve group classification problems for various classes of linear and nonlinear Schrödinger equations with an arbitrary number n of space variables.The aim of the thesis is twofold. LÄS MER

5. 4. On the existence of complex-valued harmonic morphisms

   Författare :Jonas Nordström; Matematik (naturvetenskapliga fakulteten); []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Harmonic morphisms; foliations; minimal submanifolds; Lie groups;

   Sammanfattning : This thesis consists of 4 papers, their content is described below: Paper I. We present a new method for manufacturing complex-valued harmonic morphisms from a wide class of Riemannian Lie groups. This yields new solutions from an important family of homogeneous Hadamard manifolds. LÄS MER

7. 5. Group theoretical methods for solving multidimensional nonlinear partial differential equations

   Författare :Marianna Euler; Luleå tekniska universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Mathematics; Matematik;

   Sammanfattning : New methods for constructing both exact and approximate solutions of multidimensional nonlinear partial differential equations are developed. The basis of the methods is taken from the classical Lie transformation group theory. LÄS MER