Search for dissertations about: "numerical methods in partial differential equation"

Showing result 1 - 5 of 52 swedish dissertations containing the words numerical methods in partial differential equation.

  2. 1. Numerical Methods for Wave Propagation : Analysis and Applications in Quantum Dynamics

    Author : Emil Kieri; Sverker Holmgren; Vasile Gradinaru; Hans O. Karlsson; Tobias Jahnke; Uppsala universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; computational wave propagation; quantum dynamics; time-dependent Schrödinger equation; spectral methods; Gaussian beams; splitting methods; low-rank approximation; Scientific Computing; Beräkningsvetenskap;

    Abstract : We study numerical methods for time-dependent partial differential equations describing wave propagation, primarily applied to problems in quantum dynamics governed by the time-dependent Schrödinger equation (TDSE). We consider both methods for spatial approximation and for time stepping. READ MORE

  4. 2. Numerical methods for Sylvester-type matrix equations and nonlinear eigenvalue problems

    Author : Emil Ringh; Elias Jarlebring; Johan Karlsson; Per Enqvist; Daniel Kressner; KTH; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Matrix equations; Lyapunov equation; Sylvester equation; nonlinear eigenvalue problems; two-parameter eigenvalue problems; Krylov methods; iterative methods; preconditioning; projection methods; Matrisekvationer; Lyapunovekvationen; Sylvesterekvationen; ickelinjära egenvärdesproblem; två-parameters egenvärdesproblem; Krylovmetoder; iterativa metoder; förkonditionering; projektionsmetoder; Tillämpad matematik och beräkningsmatematik; Applied and Computational Mathematics; Optimization and Systems Theory; Optimeringslära och systemteori; Numerical Analysis; Numerisk analys;

    Abstract : Linear matrix equations and nonlinear eigenvalue problems (NEP) appear in a wide variety of applications in science and engineering. Important special cases of the former are the Lyapunov equation, the Sylvester equation, and their respective generalizations. These appear, e.g. READ MORE

  5. 3. Numerical Complexity Analysis of Weak Approximation of Stochastic Differential Equations

    Author : Raul Tempone Olariaga; KTH; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; Adaptive methods; a posteriori error estimates; stochastic differential equations; weak approximation; Monte Carlo methods; Malliavin Calculus; HJM model; option price; bond market; stochastic elliptic equation; Karhunen-Loeve expansion; numerical co; Numerical analysis; Numerisk analys;

    Abstract : The thesis consists of four papers on numerical complexityanalysis of weak approximation of ordinary and partialstochastic differential equations, including illustrativenumerical examples. Here by numerical complexity we mean thecomputational work needed by a numerical method to solve aproblem with a given accuracy. 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

  7. 5. Numerical Computations with Fundamental Solutions

    Author : Per Sundqvist; Henrik Brandén; Sverker Holmgren; Alison Ramage; Uppsala universitet; []
    Keywords : NATURVETENSKAP; NATURAL SCIENCES; fundamental solution; partial differential equation; partial difference equation; iterative method; preconditioner; boundary method; Numerical Analysis; Numerisk analys;

    Abstract : Two solution strategies for large, sparse, and structured algebraic systems of equations are considered. The first strategy is to construct efficient preconditioners for iterative solvers. The second is to reduce the sparse algebraic system to a smaller, dense system of equations, which are called the boundary summation equations. READ MORE