🧮 Notes/Implementations from Numerical Methods for Engineers (Chapra/Canale)

Explore efficient algorithms in Julia for finding zeros/fixed points of functions and data interpolation. This repository provides robust and optimized solutions for common numerical analysis tasks.

数值算法的 Julia 实现

Notes for computational physics.

Affine arithmetic using sparse vector storage of coefficients

Implementation of polynomial interpolation using the Barycentric Lagrange formula with Chebyshev points. The program computes polynomial interpolants for three different functions on specified intervals, and determines the polynomial degree necessary to ensure that the error does not exceed 1e-6

Replication kit for "Asset Prices in a Huggett Economy" Krusell, Mukoyama, Smith

Analytical solutions for verification of numerical codes

Implementation of a Krylov-subspace-like solver for systems of shifted linear problems.

Make your arithmetic sharp!

A julia library for mode coupling analysis of protein simulations

Implementation of Conjugate Gradient method to solve a linear system Ax = b for sparse matrices represented by a custom data type (ScatteredArray).

FiniteElementMethod in Julia

Implementation of simulation of a mathematical pendulum's motion using the Runge-Kutta fourth-order method. Compares the pendulum's behavior with that of a harmonic oscillator and visualizes how its oscillation period varies with energy.

A Julia package for solving linear systems and optimization problems using the Conjugate Gradient method

Make some old numerical progams (mainly in Algol) run again.

Optimization Algorithms in Julia

Provides custom pure-julia numerical methods for the differentiation, interpolation, minimisation and root finding of univariate and multivariate functions.

Numerical analysis

The famous 5th order Radau IIA method, tailored for any *scalar* ODE that requires excellent solver stability