Search for dissertations about: "the Crank-Nicolson method"

Found 4 swedish dissertations containing the words the Crank-Nicolson method.

  2. 1. On Numerical Methods for the Diffusion Equation Subject to Non-Local Boundary Conditions

    Author : Gunnar Ekolin; Göteborgs universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; forward Euler method; backward Euler method; the Crank-Nicolson method; heat equation; Galerkin finite element methods; backward Euler method;

    Abstract : 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. READ MORE

  4. 2. Market Models with Stochastic Volatility

    Author : Jean-Paul Murara; Sergei Silvestrov; Guglielmo D’Amico; Mälardalens högskola; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Mathematics Applied Mathematics; matematik tillämpad matematik;

    Abstract : 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. READ MORE

  5. 3. Energy-conservative finite element methods for nonlinear Schrödinger equations

    Author : Johan Wärnegård; Patrick Henning; Xavier Antoine; KTH; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Tillämpad matematik och beräkningsmatematik; Applied and Computational Mathematics; Numerical Analysis; Numerisk analys;

    Abstract : 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. READ MORE

  6. 4. Exponential integrators for stochastic partial differential equations

    Author : Rikard Anton; David Cohen; Christian Engström; Stig Larsson; Annika Lang; Umeå universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Stochastic partial differential equations; numerical methods; stochastic exponential integrator; strong convergence; trace formulas;

    Abstract : 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. READ MORE