Advanced search

Showing result 1 - 5 of 46 essays matching the above criteria.

  1. 1. Solving Ordinary Differential Equations and Systems using Neural Network Methods

    University essay from Karlstads universitet/Institutionen för matematik och datavetenskap (from 2013)

    Author : Mimmi Westrin; [2023]
    Keywords : Neural network methods; trial solutions; numerical methods; Lotka-Volterra system; SEIR model;

    Abstract : The applications of differential equations are many. However, many differential equations modelling real-world scenarios are very complex and it can be of great difficulty to find an exact solution if one even exists. Thus, it is of importance to be able to approximate solutions of differential equations. READ MORE

  3. 2. Gravity water waves over constant vorticity flows: from laminar flows to touching waves

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

    Author : Francisco Gonçalves Jorge Dias de Carvalho; [2023]
    Keywords : Partial differential equations; Water waves; Euler equations; Free boundary problem; Bifurcation theory; Nonlinear functional analysis; Hilbert transform; Mathematics and Statistics;

    Abstract : In a recent paper, Hur and Wheeler proved the existence of periodic steady water waves over an infinitely deep, two-dimensional and constant vorticity flow and subject to gravity whose profile overhangs, among which, waves whose surface touches at a point, enclosing a bubble of air. We take this further, proving the existence of a continuous curve of water waves from a laminar flow up to a touching wave for fixed non-zero gravity. READ MORE

  4. 3. 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

  5. 4. Exploring backward stochastic differential equations and deep learning for high-dimensional partial differential equations and European option pricing

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

    Author : Jonathan Leung; [2023]
    Keywords : Backward Stochastic Differential Equations; Semilinear Parabolic Partial Differential Equations; Artificial Neural Networks; Nonlinear Option Pricing; Black-Scholes; Nonlinear Feynman-Kac; Euler-Maruyama;

    Abstract : Many phenomena in our world can be described as differential equations in high dimensions. However, they are notoriously challenging to solve numerically due to the exponential growth in computational cost with increasing dimensions. READ MORE

  6. 5. Solving Differential Equations using Data-Driven Adaptive Numerical Method

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : William Nguyen; Sirui Li; [2022]
    Keywords : ;

    Abstract : Accuracy and efficiency have always been of great concern when solving differential equations. One approach to improve accuracy is by introducing a neural network, whose role is to learn the local truncation error (LTE) of a numerical method. READ MORE