Essays about: "Partial Differential Equations"

Showing result 6 - 10 of 89 essays containing the words Partial Differential Equations.

  1. 6. Axisymmetric capillary water waves on cylindrical fluid jets

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Anna-Mariya Otsetova; [2023]
    Keywords : Euler equations; Bernoulli boundary condition; Schauder estimates; nonlinear functional analysis; Mathematics and Statistics;

    Abstract : In their paper, Vanden-Broeck, Miloh and Spivack (Wave Motion 27, 1998) describe two limiting behaviours of irrotational, axisymmetric capillary water waves using numerical methods. They found a two-parameter family of nontrivial solutions. Some solutions of small amplitude approach a uniform stream, while others approach a static configuration. READ MORE

  3. 7. Merton's Portfolio Problem under Jourdain--Sbai Model

    University essay from Mälardalens universitet/Akademin för utbildning, kultur och kommunikation

    Author : Sajedeh Saadat; [2023]
    Keywords : Merton’s Optimal Investment-Consumption Problem; Dynamic Programming; Hamilton-Jacobi-Bellman equation; Stochastic Volatility Model; Finite-difference method; Crank-Nicolson.;

    Abstract : Portfolio selection has always been a fundamental challenge in the field of finance and captured the attention of researchers in the financial area. Merton's portfolio problem is an optimization problem in finance and aims to maximize an investor's portfolio. READ MORE

  4. 8. Machine Learning Algorithms for Quantum Systems

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Oskar Fallgren; Adam Fredriksson; [2023]
    Keywords : ;

    Abstract : The Schrödinger equation is a fundamental differential equation in quantum mechanics, and solving it for general potentials is difficult even using numerical methods. In recent years, machine learning has become a popular tool for finding solutions to partial differential equations in general, and the Schrödinger equation in particular. READ MORE

  5. 9. Solving Partial Differential Equations With Neural Networks

    University essay from Uppsala universitet/Matematiska institutionen

    Author : Håkan Karlsson Faronius; [2023]
    Keywords : Partial differential equations; neural networks; physics-informed neural networks; deep ritz method; fourier neural operator; importance sampling; inverse problems;

    Abstract : In this thesis three different approaches for solving partial differential equa-tions with neural networks will be explored; namely Physics-Informed NeuralNetworks, Fourier Neural Operators and the Deep Ritz method. Physics-Informed Neural Networks and the Deep Ritz Method are unsupervised machine learning methods, while the Fourier Neural Operator is a supervised method. READ MORE

  6. 10. Implementation and study of boundary integral operators related to PDE:s in the plane

    University essay from Lunds universitet/Matematik LTH

    Author : Erik Andersson; [2023]
    Keywords : Boundary integral equation; Singular integral operator; Product integration; Close evaluation; Numerical integration; MATLAB; Mathematics and Statistics;

    Abstract : The method of solving boundary value problems of partial differential equations numerically by first reformulating the problem as a boundary integral equation has many advantages over other methods, but also some unique difficulties. Some of these difficulties stem from problems in evaluating singular or nearly singular integral operators, and solving these difficulties is an active field of research. READ MORE