Essays about: "Partial Differential Equations"

Showing result 11 - 15 of 89 essays containing the words Partial Differential Equations.

1. 11. 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

3. 12. Moving in the dark : Mathematics of complex pedestrian flows

   University essay from Karlstads universitet/Fakulteten för hälsa, natur- och teknikvetenskap (from 2013)

   Author : Meghashyam Veluvali; [2023]
   Keywords : Mathematical modelling of pedestrian dynamics; stochastic systems; evacuation time; random walk method; parabolic equation; finite difference method;

   Abstract : The field of mathematical modelling for pedestrian dynamics has attracted significant scientific attention, with various models proposed from perspectives such as kinetic theory, statistical mechanics, game theory and partial differential equations. Often such investigations are seen as being a part of a new branch of study in the domain of applied physics, called sociophysics. READ MORE

4. 13. 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

5. 14. Computational modelling of quorum sensing using cascade delay

   University essay from

   Author : Nils Axelsson; David Mårsäter; [2022]
   Keywords : Quorum sensing; URDME;

   Abstract : The scope of this project was to implement a quorum sensing model capable of synchronised oscillations from the article ”A synchronized quorum of genetic clocks” [1] in the software framework URDME [2]. The model consists of a system of partial differential equations describing time delayed and coupled biochemical reactions. READ MORE

6. 15. The Method of Characteristics

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

   Author : Ida Andersson; [2022]
   Keywords : method of characteristics; partial differential equations;

   Abstract : Differential equations, in particular partial differential equations, are used to mathematically describe many physical phenomenon. The importance of being able to solve these types of equations can therefore not be overstated. READ MORE