Pseudospectral methods for boundary value problems

Vjeran, Rađa (author), Orel, Bojan (mentor)

The purpose of this thesis is to study pseudospectral methods and to implement the algorithm that solves two point boundary value problems by pseudospectral methods. Another purpose of this thesis is to implement that algorithm into an application for solving two point boundary value problems. The rst part of the thesis presents theoretical concepts needed to understand the pseudospectral methods such as: dierential equations, boundary value problems and few more. This is followed by the theoretical idea of pseudospectral methods and algorithm in theory. The last part consists of practical implementation and explanation of how application works followed by few examples.

• Language: English
• Keywords: pseudospectral methods, boundary value problem, Python
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Publisher: [R. Vjeran]
• Year: 2015
• Number of pages: 39 str.
• PID: 20.500.12556/RUL-72322
• COBISS.SI-ID: 1536644803
• Publication date in RUL: 11.09.2015

Secondary language

• Language: Slovenian
• Title: Reševanje robnih problemov s psevdospektralnimi metodami : diplomsko delo

Abstract

Namen diplomske naloge je preučiti psevdospektralne metode in implementirati algoritem za reševanje dvotočkovnih robnih problemov. Drugi cilj diplomske naloge je implementirati ta algoritem v okviru aplikacije, ki deluje za celo množico robnih problemov v dveh točkah z uporabo programskega jezika Python. Najprej je postavljena teoretična baza: uvod v diferencialne enačbe, robni problemi ter še nekoliko konceptov potrebnih za razumevanje psevdospektralnih metod. Potem je predstavljena teoretična ideja psevdospektralnih metod in teoretičen način implementacije algoritma ter na koncu praktična realizacija in predstavitev spletne aplikacije za reševanje robnih problemov v dveh točkah.

• Keywords: psevdospektralne metode, robni problemi, Python