Search Results for "solving equations"
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Showing 68 open source projects for "solving equations"
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DifferentialEquations.jl
Multi-language suite for high-performance solvers of equations
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. The well-optimized DifferentialEquations solvers benchmark as some of the fastest implementations, using classic algorithms and ones from recent research which routinely outperform the “standard” C/Fortran methods, and include algorithms optimized for high-precision and HPC applications. ... -
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OrdinaryDiffEq.jl
High performance ordinary differential equation (ODE)
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. The well-optimized DifferentialEquations solvers benchmark as some of the fastest implementations, using classic algorithms and ones from recent research that routinely outperform the “standard” C/Fortran methods, and include algorithms optimized for high-precision and HPC applications. ... -
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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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HomotopyContinuation.jl
A Julia package for solving systems of polynomials
HomotopyContinuation.jl is a Julia package for solving systems of polynomial equations by numerical homotopy continuation. Many models in the sciences and engineering are expressed as sets of real solutions to systems of polynomial equations. We can optimize any objective whose gradient is an algebraic function using homotopy methods by computing all critical points of the objective function. -
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DeepXDE
A library for scientific machine learning & physics-informed learning
DeepXDE is a library for scientific machine learning and physics-informed learning. DeepXDE includes the following algorithms. Physics-informed neural network (PINN). Solving different problems. Solving forward/inverse ordinary/partial differential equations (ODEs/PDEs) [SIAM Rev.] Solving forward/inverse integro-differential equations (IDEs) [SIAM Rev.] fPINN: solving forward/inverse fractional PDEs (fPDEs) [SIAM J. Sci. Comput.] NN-arbitrary polynomial chaos (NN-aPC): solving forward/inverse stochastic PDEs (sPDEs) [J. ... -
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Diffrax
Numerical differential equation solvers in JAX
Diffrax is a numerical differential equation solving library built for the JAX ecosystem, with a strong focus on composability, differentiability, and high-performance scientific computing. The project provides tools for solving ordinary differential equations, stochastic differential equations, controlled differential equations, and related systems in a way that fits naturally into modern machine learning and differentiable programming workflows. ... -
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101-0250-00
ETH course - Solving PDEs in parallel on GPUs
This course aims to cover state-of-the-art methods in modern parallel Graphical Processing Unit (GPU) computing, supercomputing and code development with applications to natural sciences and engineering. -
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MathPHP
Powerful modern math library for PHP
Math PHP is a library that brings advanced mathematical functions and data analysis capabilities to PHP applications. It covers a wide range of topics, including linear algebra, calculus, statistics, probability, and numerical analysis. Math PHP is designed for developers and data scientists who require precise and efficient mathematical computations in PHP, making it suitable for scientific computing and data processing. -
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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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Xournal++
A handwriting notetaking software with PDF annotation support
Xournal++ (/ˌzɚnl̟ˌplʌsˈplʌs/) is an open-source and cross-platform note-taking software that is fast, flexible, and functional. A modern rewrite and a more feature-rich version of the wonderful Xournal program. Support for pressure-sensitive stylus and drawing tablets (Wacom, Huion, XP-Pen, etc.) Robust and customizable pen, highlighter and eraser tools, allowing you to write how you want to write. Use layers to make complex notes that are still pleasant to work with. Keep track of the... -
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SymPy
A computer algebra system written in pure Python
SymPy is an open source Python library for symbolic mathematics. Its goal is to become a full-featured computer algebra system (CAS) while maintaining the simplicity of its code. Written entirely in Python, SymPy is easy to use, comprehensible and easily extensible. It’s also very lightweight as it solely depends on mpmath, a pure Python library for arbitrary floating point arithmetic. SymPy has participated in every Google Summer of Code since 2007 and because of this has continuously... -
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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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ApproxFun.jl
Julia package for function approximation
...It is in a similar vein to the Matlab package Chebfun and the Mathematica package RHPackage. The ApproxFun Documentation contains detailed information, or read on for a brief overview of the package. The documentation contains examples of usage, such as solving ordinary and partial differential equations. The ApproxFun Examples repo contains many examples of using this package, in Jupyter notebooks and Julia scripts. Note that this is independently maintained, so it might not always be in sync with the latest version of ApproxFun. We recommend checking the examples in the documentation first, as these will always be compatible with the latest version of the package. -
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DynamicalBilliards.jl
An easy-to-use, modular, extendable and absurdly fast Julia package
A Julia package for dynamical billiard systems in two dimensions. The goals of the package is to provide a flexible and intuitive framework for fast implementation of billiard systems of arbitrary construction. -
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MultivariatePolynomials.jl
Multivariate polynomials interface
MultivariatePolynomials.jl is an implementation-independent library for manipulating multivariate polynomials. It defines abstract types and an API for multivariate monomials, terms, and polynomials and gives default implementation for common operations on them using the API. On the one hand, This packages allows you to implement algorithms on multivariate polynomials that will be independant on the representation of the polynomial that will be chosen by the user. On the other hand, it... -
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HYPRE
Parallel solvers for sparse linear systems featuring multigrid methods
Livermore’s HYPRE library of linear solvers makes possible larger, more detailed simulations by solving problems faster than traditional methods at large scales. It offers a comprehensive suite of scalable solvers for large-scale scientific simulation, featuring parallel multigrid methods for both structured and unstructured grid problems. The HYPRE library is highly portable and supports a number of languages. Work on HYPRE began in the late 1990s. It has since been used by research... -
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NeuralOperators.jl
DeepONets, Neural Operators, Physics-Informed Neural Ops in Julia
Neural operator is a novel deep learning architecture. It learns an operator, which is a mapping between infinite-dimensional function spaces. It can be used to resolve partial differential equations (PDE). Instead of solving by finite element method, a PDE problem can be resolved by training a neural network to learn an operator mapping from infinite-dimensional space (u, t) to infinite-dimensional space f(u, t). Neural operator learns a continuous function between two continuous function spaces. The kernel can be trained on different geometry, which is learned from a graph. ... -
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overtureFramework
A framework for solving partial differential equations
Overture is a framework for solving partial differential equations (PDEs) in complex, possibly moving geometry. Overture uses overlapping grids to represent the geometry. The software includes grid generation capabilities, PDE solvers for fluids, solids, and fluid-structure interactions (FSI) as well as electromagnetics. -
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LaSolv
Solves symbolic electrical AC circuit equations
In electrical engineering, AC circuits are often used in the design process. However, deriving the gain, input impedance or what have you is tedious and error prone. LaSolv takes a SPICE like description of your circuit and solves for whatever parameter you specify- voltage gain, trans-impedance, input impedance, etc. -
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Qwen2.5-Coder
Qwen2.5-Coder is the code version of Qwen2.5, the large language model
Qwen2.5-Coder, developed by QwenLM, is an advanced open-source code generation model designed for developers seeking powerful and diverse coding capabilities. It includes multiple model sizes—ranging from 0.5B to 32B parameters—providing solutions for a wide array of coding needs. The model supports over 92 programming languages and offers exceptional performance in generating code, debugging, and mathematical problem-solving. Qwen2.5-Coder, with its long context length of 128K tokens, is... -
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Fosite - advection problem solver
numerical simulation code for solving transport equations in 1D/2D/3D
Fosite is a generic framework for the numerical solution of hyperbolic conservation laws in generalized orthogonal coordinates. Its main purpose is the simulation of compressible flows in accretion disks. The underlying numerical solution method belongs to the family of unsplit conservative finite volume TVD schemes. The method is 2nd order accurate in space and uses high order Runge-Kutta and multistep schemes for time evolution. In addition to the pure advection code several source terms... -
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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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ransfoil
console to calculate airflow around an airfoil based on RANS approach
RANSFOIL is a console program to calculate airflow field around an isolated airfoil in low-speed, subsonic, transonic or supersonic regime by numerically solving the Reynolds averaged Navier-Stokes (RANS) equations using mature computational fluid dynamics (CFD) method. As postprocess results, the aerodynamic parameters of the airfoil, e.g., lift coefficient and drag coefficient, can be integrated from the airflow distribution near wall boundary. In addition, the coupling between airflow and heat transfer and the effect of surface roughness on near wall flow are considered by this program, it can be used for engineering calculation of the friction drag and heat transfer coefficients on airfoil surface. ... -
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lucidum
Application simulates the incipience of laser radiation
The dynamics of the population of energy levels and the power of stimulated radiation in laser amplifying media is modeled by solving a system of rate equations. The application was developed for students to explain the time dependence of laser power they observed. The material constants of the active medium of the laser used are specified in the configuration file. The application allows you to interactively select the pump speed and quality factor of the resonator by observing the time dependencies of the inverse population and laser radiation power. -
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MathSteps
Step by step math solutions for everyone
mathsteps is a JavaScript library that performs step-by-step algebraic simplification and equation solving for expressions provided as strings. It exposes functions to simplify expressions and to solve equations, returning a structured sequence of steps that detail each transformation. For every step, mathsteps reports the original node, the change type, the resulting node, and any substeps, which makes it useful for education, debugging, and explainable math tooling. ...
