Essays about: "nonlinear differential equation"

Showing result 1 - 5 of 27 essays containing the words nonlinear differential equation.

1. 1. Dirichlet-to-Neumann maps and Nonlinear eigenvalue problems

   University essay from KTH/Skolan för teknikvetenskap (SCI)

   Author : Tindra Jernström; Anna Öhman; [2023]
   Keywords : Dirichlet-to-Neumann maps; Nonlinear eigenvalue problems; Absorbing boundary conditions;

   Abstract : Differential equations arise frequently in modeling of physical systems, often resulting in linear eigenvalue problems. However, when dealing with large physical domains, solving such problems can be computationally expensive. READ MORE

3. 2. Evaluation of Physics Informed Neural Networks in engineering simple structural analysis problems

   University essay from Uppsala universitet/Institutionen för informationsteknologi

   Author : Georgios Nentidis; [2023]
   Keywords : ;

   Abstract : Neural Networks have found many applications for a long time in Machine Learning in different disciplines, and have especially flourished in the last decade because of the ever-increasing processing power especially from GPUs. Because of their ability to operate as universal function approximators and model nonlinear processes, attempts have been made in recent years to be also used for modeling partial differential equation (PDE) solutions. READ MORE

4. 3. 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

5. 4. Deep learning of nonlinear development of unstable flame fronts

   University essay from Lunds universitet/Institutionen för energivetenskaper

   Author : Ludvig Nobel; [2023]
   Keywords : Technology and Engineering;

   Abstract : The purpose of this study is to investigate Machine Learning methods and their ability to learn the development of nonlinear unstable flame fronts due to diffusive-thermal instabilities. This task is performed by first numerically computing long time-sequences of solutions to the chaotic partial differential equation named Kuramoto-Sivashinsky equation which models such instabilities in a flame front. READ MORE

6. 5. Solving Korteweg-de Vries equations with Discontinuous Galerkin methods

   University essay from Linköpings universitet/Tillämpad matematik; Linköpings universitet/Tekniska fakulteten

   Author : Markus Hellberg Mediaa; [2023]
   Keywords : Discontinuous Galerkin; Korteweg-de Vries; Conservation Laws; Partial Differential Equations; Numerical methods; Higher order spatial derivative; Heat Equation; Burgers’ Equation; Collocation; Lobatto Gauss Legendre; Stiffness; Nodal Approximation; Finite Volume; Finite Element;

   Abstract : In this thesis the Discontinuous Galerkin approximation performance applied to the Korteweg–de Vries equation is investigated. This equation is nonlinear with a third spatial derivative and can be used for shallow water movement. READ MORE