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Numerical Analysis

Homework Solutions for Numerical Analysis Course as Computer Science B.Sc. Student at Department of Mathematical Sciences, Sharif University of Technology.

Spring 2023

Supervisor: Dr. Mohammad Reza Razvan

Description

This repository includes my homework and projects around Numerical Analysis. There are some theoretical questions and code implementations around Numerical Methods. Most of the questions are from the sourcebook of the course: Numerical Analysis (R. Burden, Aires, A. Burden) [10th Ed.].

(my answers may be incorrect!)

Table of Implementations

some questions are implemented in Python in my homework.

Sunbect Description
Euler Method Just a simple Euler method!
Runge-Kutta-Verner Method an algorithm similar to Runge-Kutta-Fehlberg Algorithm
Adams–Bashforth Method with RK4 initializer Adams–Bashforth Method with RK4 initializer with 2,3,4,5 step
Adams–Moulton Adams–Moulton Method ( with Adams-Bashforth Corrector Support ) with different step size
3-step Adams–Moulton Method Adams–Moulton Method ( with Adams-Bashforth Corrector Support ) with different step size
Adams–Bashforth Method with Iterative Correctors Adams–Bashforth Method with p Iterative Correctors
Adams Variable Step size Predictor Corrector Adams Variable Step size Predictor Corrector with N step Adams-Bashforth and N-1 step Adams Moulton Method
Runge-Kutta Method for Systems of Differential Equations Runge-Kutta Method for Systems of Differential Equations
System with stable focus Phase Plane A simple checking on a system with stable focus and drawing its phase plane diagram
Lorenz System investigating the Lorenz system