Search Results for "nonlinear equations newton"
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Showing 38 open source projects for "nonlinear equations newton"
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VoronoiFVM.jl
Solution of nonlinear multiphysics partial differential equations
Solver for coupled nonlinear partial differential equations (elliptic-parabolic conservation laws) based on the Voronoi finite volume method. It uses automatic differentiation via ForwardDiff.jl and DiffResults.jl to evaluate user functions along with their jacobians and calculate derivatives of solutions with respect to their parameters. -
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PySINDy
A package for the sparse identification of nonlinear dynamical systems
PySINDy is a Python library that implements the Sparse Identification of Nonlinear Dynamics (SINDy) method for discovering mathematical models of dynamical systems from data. The framework focuses on identifying governing equations that describe the behavior of complex physical systems by selecting sparse combinations of candidate functions. Instead of fitting a purely predictive machine learning model, PySINDy attempts to recover interpretable differential equations that explain how a system evolves over time. ... -
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Sundials.jl
Julia interface to Sundials, including a nonlinear solver
This is a suite for numerically solving differential equations written in Julia and available for use in Julia, Python, and R. The purpose of this package is to supply efficient Julia implementations of solvers for various differential equations. -
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Theseus
A library for differentiable nonlinear optimization
Theseus is a library for differentiable nonlinear optimization that lets you embed solvers like Gauss-Newton or Levenberg–Marquardt inside PyTorch models. Problems are expressed as factor graphs with variables on manifolds (e.g., SE(3), SO(3)), so classical robotics and vision tasks—bundle adjustment, pose graph optimization, hand–eye calibration—can be written succinctly and solved efficiently. -
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ModelingToolkit.jl
Modeling framework for automatically parallelized scientific ML
ModelingToolkit.jl is a modeling language for high-performance symbolic-numeric computation in scientific computing and scientific machine learning. It then mixes ideas from symbolic computational algebra systems with causal and acausal equation-based modeling frameworks to give an extendable and parallel modeling system. It allows for users to give a high-level description of a model for symbolic preprocessing to analyze and enhance the model. Automatic symbolic transformations, such as... -
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MethodOfLines.jl
Automatic Finite Difference PDE solving with Julia SciML
MethodOfLines.jl is a Julia package for automated finite difference discretization of symbolically defined PDEs in N dimensions. It uses symbolic expressions for systems of partial differential equations as defined with ModelingToolkit.jl, and Interval from DomainSets.jl to define the space(time) over which the simulation runs. This project is under active development, therefore the interface is subject to change. The docs will be updated to reflect any changes, please check back for current... -
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Gridap.jl
Grid-based approximation of partial differential equations in Julia
Gridap provides a set of tools for the grid-based approximation of partial differential equations (PDEs) written in the Julia programming language. The library currently supports linear and nonlinear PDE systems for scalar and vector fields, single and multi-field problems, conforming and nonconforming finite element (FE) discretizations, on structured and unstructured meshes of simplices and n-cubes. It also provides methods for time integration. -
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CasADi
CasADi is a symbolic framework for numeric optimization
CasADi is a symbolic framework for numeric optimization implementing automatic differentiation in forward and reverse modes on sparse matrix-valued computational graphs. It supports self-contained C-code generation and interfaces state-of-the-art codes such as SUNDIALS, IPOPT, etc. It can be used in C++, Python, or Matlab/Octave. CasADi's backbone is a symbolic framework implementing forward and reverse modes of AD on expression graphs to construct gradients, large-and-sparse Jacobians, and... -
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NeuralPDE.jl
Physics-Informed Neural Networks (PINN) Solvers
NeuralPDE.jl is a Julia library for solving partial differential equations (PDEs) using physics-informed neural networks and scientific machine learning. Built on top of the SciML ecosystem, it provides a flexible and composable interface for defining PDEs and training neural networks to approximate their solutions. NeuralPDE.jl enables hybrid modeling, data-driven discovery, and fast PDE solvers in high dimensions, making it suitable for scientific research and engineering applications. -
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basic_numerical_methods
Didactic application to aid students in learning Numerical Methods;
A practical tool (for students and engineers) to foresee the result of calculus exercises. Calculation and visualization numerical methods for nonlinear equation, ODE, integration, linear system, polynomial fitting,..... -
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JSBSim
An open source flight dynamics & control software library
JSBSim is a multi-platform, general purpose object-oriented Flight Dynamics Model (FDM) written in C++. The FDM is essentially the physics & math model that defines the movement of an aircraft, rocket, etc., under the forces and moments applied to it using the various control mechanisms and from the forces of nature. JSBSim can be run in a standalone batch mode flight simulator (no graphical displays a.k.a. console mode) for testing and study, or integrated with the Unreal engine, FlightGear... -
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LMath library
Math library for Free Pascal and Lazarus.
...It is entirely written in Pascal and does not depend on external libraries. LMath provides routines and demo programs for numerical analysis, including mathematical functions, probabilities, matrices, optimization, linear and nonlinear equations, integration, Fast Fourier Transform, random numbers, curve fitting, statistics and graphics. It is organized s set of lazarus packages which makes it easily extensible and helps to include only really needed features in your project. -
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Ship, Tow-Tether and Moonpool Models
Linked Excel workbooks for preliminary study of the title systems
...FD and TD at the end of a file name denotes frequency domain and time domain solutions, respectively. Except for the moonpool TD model, which is a solution to the nonlinear equations of motion for the moonpool piston mode, TD solutions are obtained by superposing FD solutions in uniform random phase. Toolbars on the plot tabs can be activated to expose plot options. Model input parameters are defined in comments to the input cells of each workbook. (Use the TAB key to move between input cell.) ... -
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ME.com
Mathematical & engineering components for software development
The truth can't be complicated. Mathematical & engineering components (abbreviation ME . com) for development of the software are the comprehensive collection of original fastest algorithms for scientific computing. Not based on any known software library. Used in AtteStat, StatAnt, Criterial projects and another with rights saved include in educational purposes. Registered 2003-03-21 with the Federal Service for Intellectual Property. Completely free. No donation required. Mathematical &... -
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Magnetar Quantum Vacuum Engineering
QED Engine Quantum Vacuum Engineering
# Magnetar QED Engine ### Quantum Vacuum Engineering for Extreme Astrophysical Environments **A fully functional, real-time, closed-loop simulation of magnetar physics** Now with strong-field QED, dark photon conversion, general relativity, and force-free plasma dynamics — all in pure Python.  ## Current Capabilities (v0.5.0 – 100% complete Month-1 target) | Feature | Status | Description... -
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GiNaCDE
A software for solving Nonlinear Differential Equations
GiNaCDE is free and open-source software that solves entirely automatically linear or nonlinear differential equations. In searching traveling wave solutions, this application converts the Nonlinear Partial Differential Equations (NLPDEs) into Nonlinear Ordinary Differential Equations (NLODEs) and gives the exact solutions when they exist. The Differential Equations are solved by F-expansion and first integral methods. -
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NLIGA
Open source Matlab code for nonlinear isogeometric analysis
A unified framework, NLIGA (Non-Linear Isogeometric Analysis), is developed for mainly solving two and three-dimensional nonlinear problems on the MATLAB platform by using isogeometric analysis (IGA). Nonlinear hyperelastic and elastoplastic materials are primarily considered at this stage. Newton-Raphson method is used to solve the nonlinear governing equations. A series of benchmark examples are performed to validate the procedures. The visualization procedures are also developed to visualize the obtained results including displacements, stresses and numerical errors. ... -
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Algorithms Math Models
MATLAB implementations of algorithms
Algorithms_MathModels is a large MATLAB collection of algorithms and solved examples targeted at students and teams preparing for mathematical modeling competitions (national and international contests like MCM/ICM). The repository gathers implementations and case studies across many topics commonly used in contest solutions: optimization (linear, integer, goal and nonlinear programming), heuristic and metaheuristic methods (simulated annealing, genetic algorithms, immune algorithms), neural networks and time-series methods, interpolation and regression, graph theory, cellular automata, grey systems, fuzzy models, partial/ordinary differential equations, and multivariate analysis, among others. The codebase is organized into topic folders (e.g., HeuristicAlgorithm, IntegerProgramming, NeuralNetwork, TimeSeries) and includes dozens of worked examples and links to textbook/source materials that the author used to assemble the collection. -
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AdaAutoDiff
C++ Templates and Ada Package for Automatic Differentiation
Operators are overloaded so that a normal looking function definition provides access to not only evaluations of itself, but to evaluations of any of its analytic derivatives. Automatic differentiation means the user does not need to define the analytic expressions for all the various partial derivatives. It also means that those complex expressions are essentially calculated at compile time, and merely evaluated at runtime. First order derivatives only, forward... -
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OpenRTDynamics
A framework for implementing real-time control systems
- - - T H I S P R O J E C T M O V E D T O G I T H U B - - - A framework for the implementation of advanced real-time control systems which uses signal/block-based schematics (like Simulink) extended by several features like state machines and online-exchangeable sub-simulations. Besides, this framework properly handles multiple threads, their communication, allows to synchronise control systems to external events (e.g. variable timers or incoming network packages) and provides... -
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Programs for Numerical Methods
Didactic program to aid students in learning Numerical Methods.
...Curve fitting (Linear and Nonlinear). 8. Numerical integration (Undetermined Coefficients, Newton-Cotes, Romberg). 9. Ordinary differential equations (Euler, Runge-Kuta). -
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Gekko Timeseries Software
Timeseries handling, and solving of large-scale economic models
Gekko Timeseries Software is a free time-series oriented software package for timeseries handling, and solving and analyzing large-scale economic models. Since 2009, Gekko is being used by Danish ministeries, banks, interest groups and universities, for the simulation of economic and energy-related models. The software runs under Windows (.NET), and is open source (GNU GPL) -
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Abaqus Implementation of Phase Field
Abaqus implementation of phase--field model for brittle fracture
...This is accomplished by replacing the sharp discontinuities with a scalar damage phase-field representing the diffuse crack topology wherein the amount of diffusion is controlled by a regularization parameter. The nonlinear coupled system consisting of the linear momentum equation and a diffusion-type equation governing the phase-field evolution is solved simultaneously via a Newton–Raphson approach. The implemented crack propagation model does not require predefined paths for crack growth or user-defined surfaces to simulate crack debonding. http://dx.doi.org/10.1016/j.commatsci.2014.05.071 -
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OptimC
OptimC - Optimization / Unconstrained Minimization Library in ANSI C
OptimC is a C software package to minimize any unconstrained multivariable function. The algorithms implemented are Nelder-Mead,Newton Methods (Line Search and Trust Region methods), Conjugate Gradient and BFGS (regular and Limited Memory). Brent method is also available for single variable functions if the bounds are known. Update 06/09/2014 - Nonlinear Squares Implementation [Levenberg-Marquardt Method] Added. Documentation - http://code.google.com/p/optimc/ -
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NumMath
Numerical methods calculation with graphs
Math is a program designed to calculate roots of nonlinear equation, roots of system of linear equations, differentiate, integrate, approximate using LMS, matrix calculation using numerical methods for calculating results, estimated errors and much more. Math is also capable of drawing standard functions using graph dialog window to help with visualization functions, results, or approximation with given points and much more.
