numerical_methods_2026

This repository contains implementations of classical numerical methods as part of a university course. Almost every lab assignment focuses on applying mathematical methods to real or simulated data.

Repository structure

• lab0/ - introductory task
• lab1/ - the use of cubic spline interpolation to construct a smooth elevation profile based on real-world geodata
• lab2/ - using Newton's interpolation to approximate CPU load based on limited data
• lab3/ - least-squares approximation for forecasting the average monthly temperature
• lab4/ - numerical differentiation of a moisture model using finite differences with Runge-Romberg and Aitken refinements; step-size optimization and error analysis
• lab5/ - numerical integration using Simpson’s method and its refinements by Runge-Römbberg, Eitken and an adaptive algorithm
• lab6/ - solving linear systems using LU decomposition and Gaussian elimination
• lab7/ - solving linear systems using iterative methods: simple iteration, Jacobi, and Gauss-Seidel
• lab8/ - several numerical methods for solving nonlinear equations with a single unknown, in particular those with complex roots
• lab9/ - solving a system of nonlinear equations using the Hooke–Jeeves zero-order method
• lab10/ - solving ordinary differential equations using the Runge-Kutta method and the Adams-Bashforth-Moulton method, with error analysis and adaptive step size control

Requirements

• Python 3.10+
  • numpy
  • matplotlib
  • requests

Notes

• Input data files are stored inside each lab directory.
• Some labs contain helper scripts (for example, tabulation utilities) that can be run separately.