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Numerical Analysis

A collection of algorithms in numerical analysis implemented in C++. https://numcollect.musicscience37.com/

Programmable console calculator

Leonardus is an open source project. It is a minimalist, stack-based programming system designed as a flexible framework for implementing and exploring algorithms. The syntax and semantics of its scripting language, LeoScript, are inspired by PostScript and Forth. It is extended with a prototype-based, object-oriented paradigm, has seamless integration into JupyterLab and Docker, and provides a concise and expressive environment for learning and experimentation.

The project name is a nod to Leonardus Pisanus, who was named and became known as Fibonacci.

Consult the project's GitLab Pages for documentation.

Fatou sets in Julia (Fractals, Newton basins, Mandelbrot)

数値解析で調査したことをまとめる。 https://numanalnote.musicscience37.com/

Adaptive P/ODE numerics with Grassmann element TensorField assembly

Toolkit for studying numerical analysis and floating point algebra round-off

This repository contains the MATLAB codes for the numerical approximation of the (basic and type) reproduction numbers of linear time-periodic ODE systems. This package allows full flexibility in splitting the model coefficients into ''birth'' and ''transition'' processes. R0_PeriodicODEs computes the pseudospectral discretization of the birth and transition operators B and M, namely BN and MN, obtained from the original time-periodic ODE system by applying the theory of evolution semigroups. Then, the approximation of the relevant reproduction number is obtained through the spectral radius of the approximating ''Next-Generation matrix'' BN*MN^(-1).

Solving second-order elliptic Partial Differential Equations (PDE) using Isogeometric Finite Element Methods (IG-FEM) with Non-uniform rational basis splines (NURBS) mappings of piece-wise polynomial basis functions. Convergence and spatial regularity guaranteed.

numerical methods

Revelations 1: A simple question about Newton's method with an unbelievably weird answer

What happens when we make a color-coded scatter plot of which zero a point converges to under Newton's method?

A simple C-library for linear algebra operation : LU decomposition, QR decomposition, etc.

Header files with functions I wrote and collected for CS407, Numerical Analysis

Originally written to solve systems of integro-differential equations via collocation method in arbitrary number of variables. The current implementation of the method is based on a finite dimensional orthogonal system of functions.