Uporaba integracijskega pristopa za eksplicitno reševanje diferencialnih enačb

Barukčić, Matej (author), Halilovič, Miroslav (mentor)

Cilj zaključne naloge je razviti integracijsko metodo za eksplicitne diferencialne enačbe z namenom, da bi izboljšali natančnost obstoječih diferencialnih metod, ki se uporabljajo za obravnavanje dinamičnih problemov. Primarno se uporabljajo metode Runge-Kutta 4. reda, ki izhajajo iz Runge-Kutta 1. reda oziroma iz Eulerjeve metode. Slabost raznih variacij metod Runge-Kutta je običajno v tem, da je potrebno obravnavan problem, v primeru, da je popisan z diferencialno enačbo 2. reda, prevesti v sistem diferencialnih enačb 1. reda. Razvita integracijska metoda temelji na eksplicitnem reševanju z uporabo nastavkov za rešitev diferencialne enačbe, ki je odsekoma izpolnjena integralno. Z razvito integracijsko metodo želimo omenjeno slabost obstoječih metod odpraviti, seveda pa se moramo zavedati, da ima tudi takšen pristop prednosti in slabosti, ki so v delu predstavljene.

• Language: Slovenian
• Keywords: numerične metode numerična integracija reševanje diferencialnih enačb eksplicitno reševanje DE metoda Runge-Kutta reševanje dinamskih problemov
• Work type: Bachelor thesis/paper
• Organization: FS - Faculty of Mechanical Engineering
• Year: 2017
• PID: 20.500.12556/RUL-94928
• Publication date in RUL: 11.09.2017

Secondary language

• Language: English
• Title: Use of integration approach for explicit solving differential equations

Abstract

The aim of the current work is to develop an integration method for explicit differential equations in order to improve the accuracy of the existing differential methods used to deal with dynamic problems. Primary methods for solving are Runge-Kutta 4th order, which are derived from the Runge-Kutta 1st order or Euler method. The disadvantage of various variations of the Runge-Kutta methods is usually that when solving one real problem, which is written with the differential equation of the second order, must be translated into the differential equations of the 1st order. Our integration method is based on an explicit solution with predefined initial conditions or with an extension to solve a differential equation. With our integration method, we wish to eliminate this weakness, but of course we must be aware that such an approach also has the advantages and disadvantages that are presented in the presented work.

• Keywords: numerical methods numerical integration solving differential equations explicit solving DE method Runge-Kutta dynamic problem solving