Sökning: "ordinary differential equation"

Visar resultat 1 - 5 av 45 avhandlingar innehållade orden ordinary differential equation.

1. 1. Variational Methods for Moments of Solutions to Stochastic Differential Equations

   Författare :Kristin Kirchner; Chalmers tekniska högskola; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Additive and multiplicative noise; Stochastic partial differential equation; Projective and injective tensor product space; Hilbert tensor product space; Space-time variational problem; Petrov-Galerkin discretization; Stochastic ordinary differential equation;

   Sammanfattning : Numerical methods for stochastic differential equations typically estimate moments of the solution from sampled paths. Instead, we pursue the approach proposed by A. Lang, S. Larsson, and Ch. LÄS MER

3. 2. Titchmarsh-Weyl M-function asymptotics and some results in the inverse spectral theory for vector-valued Sturm-Liouville equations and a certain higher order ordinary differential equation

   Författare :Erik Andersson; Matematik (naturvetenskapliga fakulteten); []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Functions; differential equations; Funktioner; differentialekvationer; Paley-Wiener.; The generalized Fourier transform; A certain higher order ordinary differential equation; Borg-Marchenko theorems; Vector-valued Sturm-Liouville equations; Inverse spectral theory; Titchmarsh-Weyl M-function asymptotics; Asymptotics of solutions; Spectral measure;

   Sammanfattning : This discourse is constituted by two separate reprots, where the first one offers an elementary deduction of the leading order term asymptotics for the Titchmarsh-Weyl M-function corresponding to a vector-valued Sturm-Liouville equation of the form -(PU')'+QU=zu, xin[0,b), with P^{-1},W,Q being hermitean with locally integrable entries; and under some additional conditions on P^{-1} and W. In the special case of P=W=I, we give some further asymptotic results for the same M-function. LÄS MER

4. 3. Differential Equations with Constraints

   Författare :Olivier Verdier; Matematik LTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

   Sammanfattning : We study various differential equations subject to constraints. In the first part we study a partial differential equation, Burgers equation, subject to time-periodicity constraint. The forcing term is time-periodic and may be highly irregular. LÄS MER

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

   Författare :Raul Tempone Olariaga; KTH; []
   Nyckelord :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;

   Sammanfattning : 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. LÄS MER

7. 5. Approximation of Optimally Controlled Ordinary and Partial Differential Equations

   Författare :Mattias Sandberg; Anders Szepessy; Nils-Henrik Risebro; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; MATHEMATICS; MATEMATIK;

   Sammanfattning : In this thesis, which consists of four papers, approximation of optimal control problems is studied. In Paper I the Symplectic Pontryagin method for approximation of optimally controlled ordinary differential equations is presented. LÄS MER