This repository contains the software implementation for my Bachelor's thesis, "Numerical Methods for Solving Differential-Algebraic Equations" , completed at the Warsaw University of Technology (Mathematics and Data Analysis, 2024). The thesis was defended with Honors. You can find the thesis in this repository. It is written in polish.
The primary objective of this project is to efficiently solve systems of Differential-Algebraic Equations (DAEs) of the general form
To achieve high algorithmic stability and computational efficiency, the solver utilizes the Backward Differentiation Formula (BDF). The core computational engine is written entirely in C++ to ensure maximum performance, while Python is utilized to drive the simulations and visualize the results.
The repository is divided into two main environments: the high-performance solver and the visualization scripts.
Contains the C++ source code. Visit the /cpp directory to compile the DAE solver from scratch.
If you want to skip the compilation and directly explore the results, navigate to the /python directory. Here you will find scripts that interact with the compiled DAE-Solver to generate plots and animations.
Below are the visual outputs generated by the solver, demonstrating its stability and accuracy on double pendulum problem.