Search Results for "interval"

This package provides guaranteed methods for finding roots of functions, i.e. solutions to the equation f(x) == 0 for a function f. To do so, it uses methods from interval analysis, using interval arithmetic from the IntervalArithmetic.jl package by the same authors. The basic function is roots. A standard Julia function and an interval is provided and the roots function return a list of intervals containing all roots of the function located in the starting interval.

IntervalArithmetic.jl is a Julia package for validated numerics in Julia. All calculations are carried out using interval arithmetic where quantities are treated as intervals. The final result is a rigorous enclosure of the true value. We are working towards having the IntervalArithmetic library be conformant with the IEEE 1788-2015 Standard for Interval Arithmetic. To do so, we have incorporated tests from the ITF1788 test suite.

...The find_zero function provides the primary interface. The basic call is find_zero(f, x0, [M], [p]; kws...) where, typically, f is a function, x0 a starting point or bracketing interval, M is used to adjust the default algorithms used, and p can be used to pass in parameters. Bisection-like algorithms. For functions where a bracketing interval is known (one where f(a) and f(b) have alternate signs), a bracketing method, like Bisection, can be specified. The default is Bisection, for most floating point number types, employed in a manner exploiting floating point storage conventions. ...

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 usage information.

ApproxFun is a package for approximating functions. 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...

...The package provides three basic functions: quadgk, gauss, and kronrod. quadgk performs the integration, gauss computes Gaussian quadrature points and weights for integrating over the interval [a, b], and kronrod computes Kronrod points, weights, and embedded Gaussian quadrature weights for integrating over [-1, 1].