Essays about: "Euler Method"

Showing result 1 - 5 of 74 essays containing the words Euler Method.

  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. Structural responses due to underwater detonations : Validation of explosion modelling methods using LS-DYNA

    University essay from Linköpings universitet/Mekanik och hållfasthetslära

    Author : Gustav Blomgren; Ebba Carlsson; [2023]
    Keywords : Underwater explosion; UNDEX; detonation; fluid structure interaction; FSI; SSA; S-ALE; shock-wave; explosive; PETN; explosive modelling; Sub-Sea Analysis; Structured ALE; Arbitrary Lagrangian Euler; Multi Material Arbitrary Lagrangian Euler; MMALE; LS-DYNA;

    Abstract : Modelling the full event of an underwater explosion (UNDEX) is complex and requires advanced modelling methods in order to achieve accurate responses. The process of an UNDEX includes a series of events that has to be considered. READ MORE

  4. 3. 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

  5. 4. 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

  6. 5. The role of explicit solutions in the analysis of epidemic models

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Kosay Hatem; [2022]
    Keywords : Epidemic models; explicit solutions; numerical solutions;

    Abstract : In this thesis, we will study basic mathematical epidemic models SIR, SIS, and SEIR. Then we will construct a modified model as a combination of SIR and SIS models. First, we will find the explicit solutions for the SIS model. and show no exact solution for the SIR model. READ MORE