Sökning: "the Crank-Nicolson method"
Hittade 4 avhandlingar innehållade orden the Crank-Nicolson method.
1. On Numerical Methods for the Diffusion Equation Subject to Non-Local Boundary Conditions
Sammanfattning : In the first paper three different finite difference methods for solving the heat equation in one space dimension with boundary conditions containing integrals over the interior of the interval are considered. The schemes are based on the forward Euler, the backward Euler and the Crank-Nicolson methods. Error estimates are derived in maximum norm. LÄS MER
2. Market Models with Stochastic Volatility
Sammanfattning : Financial Markets is an interesting wide range area of research in Financial Engineering. In this thesis, which consists of an introduction, six papers and appendices, we deal with market models with stochastic volatility in order to understand some financial derivatives, mainly European options. LÄS MER
3. Energy-conservative finite element methods for nonlinear Schrödinger equations
Sammanfattning : This thesis is devoted to numerical methods for nonlinear Schrödingerequations (NLSEs). These equations have applications in a variety offields such as optics, fluid dynamics, solid-state physics and, of course,quantum mechanics. Notably, the cubic NLSE describes the dynamics of Bose-Einstein condensates. LÄS MER
4. Exponential integrators for stochastic partial differential equations
Sammanfattning : Stochastic partial differential equations (SPDEs) have during the past decades become an important tool for modeling systems which are influenced by randomness. Because of the complex nature of SPDEs, knowledge of efficient numerical methods with good convergence and geometric properties is of considerable importance. LÄS MER