{"id":25644043,"url":"https://github.com/nirupamkhanal/numericalanalysis","last_synced_at":"2025-11-13T18:02:01.466Z","repository":{"id":252263382,"uuid":"839909768","full_name":"NirupamKhanal/NumericalAnalysis","owner":"NirupamKhanal","description":"Numerical Methods for Computational Mathematics and Analysis","archived":false,"fork":false,"pushed_at":"2025-02-05T04:59:35.000Z","size":603,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-02-05T05:27:36.370Z","etag":null,"topics":["analysis","bisection-method","extrapolation","interpolation-methods","lagrange-interpolation","linear-algebra","linear-programming","monte-carlo","montecarlo-simulation","navier-stokes-equations","newton-cotes","numerical-analysis","numerical-calculus","numerical-integration","numerical-methods","numericalanalysis","optimization-algorithms","ordinary-differential-equations","partial-differential-equations","trapezoidal-method"],"latest_commit_sha":null,"homepage":"","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/NirupamKhanal.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2024-08-08T15:12:15.000Z","updated_at":"2025-02-05T04:59:39.000Z","dependencies_parsed_at":"2024-12-16T21:22:04.771Z","dependency_job_id":"7860f644-598f-47eb-9613-2f3468bdf5e9","html_url":"https://github.com/NirupamKhanal/NumericalAnalysis","commit_stats":null,"previous_names":["nirupamkhanal/numericalanalysis"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/NirupamKhanal%2FNumericalAnalysis","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/NirupamKhanal%2FNumericalAnalysis/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/NirupamKhanal%2FNumericalAnalysis/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/NirupamKhanal%2FNumericalAnalysis/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/NirupamKhanal","download_url":"https://codeload.github.com/NirupamKhanal/NumericalAnalysis/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":240285474,"owners_count":19777296,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["analysis","bisection-method","extrapolation","interpolation-methods","lagrange-interpolation","linear-algebra","linear-programming","monte-carlo","montecarlo-simulation","navier-stokes-equations","newton-cotes","numerical-analysis","numerical-calculus","numerical-integration","numerical-methods","numericalanalysis","optimization-algorithms","ordinary-differential-equations","partial-differential-equations","trapezoidal-method"],"created_at":"2025-02-23T07:31:02.796Z","updated_at":"2025-11-13T18:01:56.429Z","avatar_url":"https://github.com/NirupamKhanal.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Numerical Analysis \n\nThis repository contains various numerical methods and algorithms implemented in a variety of programming languages, including Julia, MATLAB, Python, and Fortran. The code is organized into different sections according to topics like interpolation, optimization, root-finding algorithms, linear algebra, and more.\n\n## Table of Contents\n- [Interpolation and Extrapolation](#interpolation-and-extrapolation)\n- [Linear Algebra](#linear-algebra)\n- [Monte Carlo Simulations](#monte-carlo-simulations)\n- [Navier-Stokes Equations](#navier-stokes-equations)\n- [Numerical Differentiation and Integration](#numerical-differentiation-and-integration)\n- [Optimization](#optimization)\n- [Ordinary Differential Equations (ODEs)](#ordinary-differential-equations-odes)\n- [Partial Differential Equations (PDEs)](#partial-differential-equations-pdes)\n- [Root-Finding Algorithms](#root-finding-algorithms)\n- [License](#license)\n\n## Interpolation and Extrapolation\nInterpolation and extrapolation are techniques to estimate unknown values between or beyond a set of known data points. The following methods are implemented:\n\n- **Cubic Spline Interpolation** (`CubicSplineInterpolation.jl`)\n- **Hermite Interpolation** (`Hermitelnterpolation.jl`)\n- **Lagrange Interpolation** (`Lagrangelnterpolation.f90`)\n- **Linear Spline Interpolation** (`LinearSplineInterpolation.jl`)\n- **Newton’s Backward Interpolation** (`NewtonsBackwardInterpolation.m`)\n- **Newton’s Divided Differences** (`NewtonsDividedDifferencesInterpolation.jl`)\n- **Newton’s Forward Interpolation** (`NewtonsForwardInterpolation.m`)\n- **Quadratic Spline Interpolation** (`QuadraticSplineInterpolation.jl`)\n- **General Spline Interpolation in Python** (`SplineInterpolation.py`)\n\nUse Cases: These methods are commonly used in numerical computing for curve fitting and data smoothing.\n\n## Linear Algebra\nLinear algebra algorithms are fundamental for solving systems of equations and matrix operations.\n\n- **Gauss Jordan Method** (`GaussJordan.m`)\n- **Gauss-Seidel Method** (`GaussSeidel.m`)\n- **Jacobi Method** (`Jacobi.m`)\n- **LU Decomposition (Cholesky's Method)** (`LUCholeskysMethod.m`)\n- **LU Decomposition (Crout's Method)** (`LUCroutsMethod.m`)\n- **LU Decomposition (Doolittle's Method)** (`LUDoolittleMethod.m`)\n- **Power Method** (`PowerMethod.m`)\n\nUse Cases: These methods are often used in solving linear systems, matrix decomposition, and eigenvalue problems.\n\n## Monte Carlo Simulations\nMonte Carlo methods are used to perform numerical integration and simulate random processes.\n\n- **1D Monte Carlo Simulation** (`MonteCarlo1d.py`)\n- **2D Monte Carlo Simulation** (`MonteCarlo2d.py`)\n- **Monte Carlo Markov Chains** (`MonteCarloMarkovChains.ipynb`)\n\nUse Cases: Widely used in numerical integration, stochastic modeling, and simulations in physics and finance.\n\n## Navier-Stokes Equations\nThis section contains implementations for solving the Navier-Stokes equations, primarily in fluid dynamics.\n\n- **CFD: Lid Driven Cavity Problem** (`CFD_Lid_Driven_Cavity.py`)\n\nUse Cases: These equations describe the motion of viscous fluid substances and are used in computational fluid dynamics (CFD).\n\n## Numerical Differentiation and Integration\nNumerical methods for differentiation and integration are useful for approximating the results of derivatives and integrals.\n\n- **Gaussian Quadrature** (`GaussianQuadrature.f90`, `GaussianQuadrature.m`)\n- **Monte Carlo Integration (1D)** (`MonteCarlolntegration1d.f90`)\n- **Monte Carlo Integration (2D)** (`MonteCarlolntegration2d.f90`)\n- **Simpson's Rule** (`SimpsonsRule.f90`)\n- **Trapezoidal Rule** (`TrapezoidalRule.f90`)\n\nUse Cases: These methods are crucial for numerical integration when exact methods are impractical.\n\n## Optimization\nOptimization techniques help in finding maxima, minima, or optimal solutions.\n\n- **Linear Programming (Big-M Method)** (`BigM.m`)\n- **Dual Simplex Method** (`DualSimplex.m`)\n- **Graphical Method** (`GraphicalMethod.m`)\n- **Simplex Method** (`Simplex.m`)\n- **Gradient Descent for Linear Problems** (`GradDescentLin.ipynb`)\n\nUse Cases: These methods are widely used in operational research, machine learning, and economics to solve optimization problems.\n\n## Ordinary Differential Equations (ODEs)\nMethods for numerically solving ordinary differential equations.\n\n- **Euler's Method (Fortran)** (`EulersMethod.f90`)\n- **Euler's Method (Python)** (`EulersMethod.py`)\n- **Runge-Kutta 2nd Order Method** (`RungeKutta2ndOrder.f90`)\n- **Runge-Kutta 4th Order Method** (`RungeKutta4thOrder.f90`)\n\nUse Cases: These methods are widely used in physics, engineering, and biological modeling to solve time-dependent processes.\n\n## Partial Differential Equations (PDEs)\nPDEs describe functions with multiple variables and their partial derivatives.\n\n- **Crank-Nicholson Method** (`CrankNicholsonMethod.m`)\n- **DuFort-Frankel Method** (`DuFortFrankelMethod.m`)\n- **Backward Time Central Space (BTCS) for Heat Equation** (`PDE-BTCS-HeatEquation.m`)\n- **Forward Time Central Space (FTCS) for Heat Equation** (`PDE-FTCS-HeatEquation.m`)\n- **Richardson Method** (`RichardsonMethod.m`)\n\nUse Cases: PDEs are used in modeling heat transfer, fluid dynamics, and electromagnetism.\n\n## Root-Finding Algorithms\nAlgorithms for finding roots of nonlinear equations.\n\n- **Bisection Method** (`Bisection.f90`)\n- **Fixed Point Iteration** (`FixedPointlteration.m`)\n- **Newton-Raphson Method** (`NewtonRaphson.f90`)\n- **Regula Falsi Method** (`Regula-Falsi.m`)\n- **Secant Method** (`SecantMethod.f90`)\n\nUse Cases: Used in numerical analysis to solve equations in engineering and science problems.\n\n## License\nThis project is licensed under the Apache 2.0 License. See the [LICENSE](./LICENSE) file for details.\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fnirupamkhanal%2Fnumericalanalysis","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fnirupamkhanal%2Fnumericalanalysis","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fnirupamkhanal%2Fnumericalanalysis/lists"}