# \#approxfun

**URL:** https://discourse.julialang.org/tag/approxfun/913.md

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## [Eigen value and eigen functions of linear operator](https://discourse.julialang.org/t/eigen-value-and-eigen-functions-of-linear-operator/133859)

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**Author:** [@Liris](https://discourse.julialang.org/u/Liris)\
**Replies:** 19\
**Last updated:** [January 28, 2026, 9:20am UTC](https://discourse.julialang.org/t/eigen-value-and-eigen-functions-of-linear-operator/133859 "2026-01-28T09:20:20Z")

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I am doing the linear stability analysis of a system of equations representing a free surface flow, which typically ends up with a generalised eigenvalue problem of the form: L\_{1} X = \\lambda p(z) u L\_{2} X = \\lambda …

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## [Speeding up combination of Funs](https://discourse.julialang.org/t/speeding-up-combination-of-funs/129400)

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**Author:** [@nilsbecker](https://discourse.julialang.org/u/nilsbecker)\
**Replies:** 15\
**Last updated:** [June 11, 2025, 1:28pm UTC](https://discourse.julialang.org/t/speeding-up-combination-of-funs/129400 "2025-06-11T13:28:48Z")

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I’m building up an ApproxFun.Fun by successively multiplying a lot of individual factors along a graph. The individual factors are themselves also Funs. The situation is similar to this fake code factors = \[\] for n in …

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## [Nonlinear boundary conditions in ApproxFun](https://discourse.julialang.org/t/nonlinear-boundary-conditions-in-approxfun/129504)

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**Author:** [@MingjiaYan](https://discourse.julialang.org/u/MingjiaYan)\
**Replies:** 0\
**Last updated:** [May 31, 2025, 3:43pm UTC](https://discourse.julialang.org/t/nonlinear-boundary-conditions-in-approxfun/129504 "2025-05-31T15:43:07Z")

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Hi, I’m trying to solve for the steady state solution of a one-dimensional heat equation describing a nonlinear heat conduction in a finite domain \[0,1\] using ApproxFun.jl: T\_{xx} = 0 subject to a Dirichlet boundary c…

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## [Integrating over piecewise approxfun](https://discourse.julialang.org/t/integrating-over-piecewise-approxfun/127309)

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**Author:** [@nilsbecker](https://discourse.julialang.org/u/nilsbecker)\
**Replies:** 8\
**Last updated:** [March 25, 2025, 4:08pm UTC](https://discourse.julialang.org/t/integrating-over-piecewise-approxfun/127309 "2025-03-25T16:08:26Z")

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Following up on my earlier post, I now have an ApproxFun.jl Fun defined over a piecewise domain: using ApproxFun f\_pw = Fun(x -\> (x \< 1.0 ? exp(x) : 1.), union(Segment(0.,1.), Segment(1.,2.))) f\_pw\_i = integrate(f\_pw) T…

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## [Truncated power series in ApproxFun.jl](https://discourse.julialang.org/t/truncated-power-series-in-approxfun-jl/124593)

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**Author:** [@Domenico\_Lahaye](https://discourse.julialang.org/u/Domenico_Lahaye)\
**Replies:** 10\
**Last updated:** [January 11, 2025, 1:09pm UTC](https://discourse.julialang.org/t/truncated-power-series-in-approxfun-jl/124593 "2025-01-11T13:09:04Z")

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I gave ApproxFun.jl another look. As far as I can see, polynomials of truncated power series in ApproxFun.jl (requires for e.g. the Duffing equation) are poorly documented. Do I overlook something?

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## [ApproxFun: Derivative: Set vs. Unset space](https://discourse.julialang.org/t/approxfun-derivative-set-vs-unset-space/124601)

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**Author:** [@Domenico\_Lahaye](https://discourse.julialang.org/u/Domenico_Lahaye)\
**Replies:** 3\
**Last updated:** [January 10, 2025, 7:30am UTC](https://discourse.julialang.org/t/approxfun-derivative-set-vs-unset-space/124601 "2025-01-10T07:30:45Z")

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Regarding ApproxFun.jl (likely more general): what is the rationale (guideline or rule of thumb) for setting or unsetting the space for the Derivative function?

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## [\[ANN\] PeriodicMatrices.jl - Handling of periodic time-varying matrices](https://discourse.julialang.org/t/ann-periodicmatrices-jl-handling-of-periodic-time-varying-matrices/124425)

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**Author:** [@andreasvarga](https://discourse.julialang.org/u/andreasvarga)\
**Replies:** 4\
**Last updated:** [January 7, 2025, 7:24am UTC](https://discourse.julialang.org/t/ann-periodicmatrices-jl-handling-of-periodic-time-varying-matrices/124425 "2025-01-07T07:24:03Z")

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PeriodicMatrices.jl provides the basic tools to handle periodic time-varying matrices. This package is the basis for developing the PeriodicMatrixEquations.jl and PeriodicSystems.jl packages. For a real periodic matrix A…

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## [Speed of ApproxFun.jl solution to Screened Poisson in cylindrical coordinates](https://discourse.julialang.org/t/speed-of-approxfun-jl-solution-to-screened-poisson-in-cylindrical-coordinates/105565)

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**Author:** [@parb](https://discourse.julialang.org/u/parb)\
**Replies:** 2\
**Last updated:** [October 30, 2023, 8:26pm UTC](https://discourse.julialang.org/t/speed-of-approxfun-jl-solution-to-screened-poisson-in-cylindrical-coordinates/105565 "2023-10-30T20:26:28Z")

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The examples of ApproxFun.jl examples solutions are fascinating and powerful, and I’d love to figure out the best performance for solving the homogeneous screened Poisson equation but in cylindrical coordinates (with cir…

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## [How to solve volterra integral equation of second kind?](https://discourse.julialang.org/t/how-to-solve-volterra-integral-equation-of-second-kind/94332)

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**Author:** [@Jian\_ZUO](https://discourse.julialang.org/u/Jian_ZUO)\
**Replies:** 21\
**Last updated:** [September 19, 2023, 8:39am UTC](https://discourse.julialang.org/t/how-to-solve-volterra-integral-equation-of-second-kind/94332 "2023-09-19T08:39:00Z")

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Hi everyone, I need to solve a Volterra integral equation as follows: Here f(y) and K(x, y) are known functions (nonlinear) As an example, take f(y) = 3x^3; K(x, y) = 1 - exp(x). I saw this post about solving Volt…

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## [ApproxFun.jl Spectral method for 2D Helmholtz equation on unbounded domains](https://discourse.julialang.org/t/approxfun-jl-spectral-method-for-2d-helmholtz-equation-on-unbounded-domains/102255)

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**Author:** [@mleprovost](https://discourse.julialang.org/u/mleprovost)\
**Replies:** 2\
**Last updated:** [August 21, 2023, 5:50pm UTC](https://discourse.julialang.org/t/approxfun-jl-spectral-method-for-2d-helmholtz-equation-on-unbounded-domains/102255 "2023-08-21T17:50:00Z")

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Hello, I would like to solve the following homogeneous Helmholtz problem with a spectral method on an 2D unbounded domain: (i \\alpha - \\Delta) \\hat{\\omega} = 0, \\;\\alpha \> 0 with a Dirichlet boundary condition for th…

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## [Using Numerical Integration and ApproxFun in Turing.jl](https://discourse.julialang.org/t/using-numerical-integration-and-approxfun-in-turing-jl/101850)

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**Author:** [@dlakelan](https://discourse.julialang.org/u/dlakelan)\
**Replies:** 12\
**Last updated:** [July 21, 2023, 5:13pm UTC](https://discourse.julialang.org/t/using-numerical-integration-and-approxfun-in-turing-jl/101850 "2023-07-21T17:13:09Z")

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I’m trying to write some code to “show how it works” when it comes to imposing high quality prior information on a Bayesian regression problem. I’m running into implementation issues and could use some thoughts @stevengj …

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## [Higher accuracy in numerical cumulative integration](https://discourse.julialang.org/t/higher-accuracy-in-numerical-cumulative-integration/96898)

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**Author:** [@roi.holtzman](https://discourse.julialang.org/u/roi.holtzman)\
**Replies:** 15\
**Last updated:** [April 1, 2023, 7:35pm UTC](https://discourse.julialang.org/t/higher-accuracy-in-numerical-cumulative-integration/96898 "2023-04-01T19:35:42Z")

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There are some threads about numerical cumulative integration like this and this. However, I have a more basic question. I am interested in performing the integral S(x; a) = \\int\_a^x f(x') dx' where x \\le b. Note that f…

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## [How to fit a polynomial with a pre-determined degree to a set of points?](https://discourse.julialang.org/t/how-to-fit-a-polynomial-with-a-pre-determined-degree-to-a-set-of-points/91981)

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**Author:** [@Hugo](https://discourse.julialang.org/u/Hugo)\
**Replies:** 7\
**Last updated:** [December 27, 2022, 7:44pm UTC](https://discourse.julialang.org/t/how-to-fit-a-polynomial-with-a-pre-determined-degree-to-a-set-of-points/91981 "2022-12-27T19:44:06Z")

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Hi, all I want to approximate a function to a vector v of 99 values so I can evaluate that function over other values. This can be a simple linear interpolation of the 99 values, but I’d fit a polynomial in case other v…

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## [Solving 2D poisson equation in polar coordinates (finite differences)](https://discourse.julialang.org/t/solving-2d-poisson-equation-in-polar-coordinates-finite-differences/74280)

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**Author:** [@Aran](https://discourse.julialang.org/u/Aran)\
**Replies:** 19\
**Last updated:** [June 7, 2022, 1:47am UTC](https://discourse.julialang.org/t/solving-2d-poisson-equation-in-polar-coordinates-finite-differences/74280 "2022-06-07T01:47:03Z")

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Hello all, I am looking to solve the following poisson equation \\nabla^2 \\psi = -\\omega \\quad \\text{and} \\quad \\nabla^2 = \\frac{\\partial ^2}{{\\partial \\rho^2 }} + \\frac{1}{\\rho }\\frac{\\partial}{\\partial \\rho} + \\frac{…

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## [Changing domain for Fourier](https://discourse.julialang.org/t/changing-domain-for-fourier/85331)

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**Author:** [@andreasvarga](https://discourse.julialang.org/u/andreasvarga)\
**Replies:** 5\
**Last updated:** [August 9, 2022, 5:52am UTC](https://discourse.julialang.org/t/changing-domain-for-fourier/85331 "2022-08-09T05:52:02Z")

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I am using ApproxFun.jl as basis to define and manipulate periodic matrices within the PeridicSystems.jl, a collection of tools dedicated for handling periodic systems. I consider ApproxFun.jl a valuable tool for my purp…

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## [ApproxFun and Burgers' equation](https://discourse.julialang.org/t/approxfun-and-burgers-equation/84660)

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**Author:** [@DanielVandH](https://discourse.julialang.org/u/DanielVandH)\
**Replies:** 6\
**Last updated:** [July 26, 2022, 8:22pm UTC](https://discourse.julialang.org/t/approxfun-and-burgers-equation/84660 "2022-07-26T20:22:11Z")

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I am trying to use ApproxFun to solve Burgers’ equation, u\_t + uu\_x = \\mu u\_{xx}, on the interval -L \\leq x \\leq L with initial condition u(x, 0) = f(x) = 1/(1+x^2) and boundary conditions u(\\pm L, t) = 0. I was trying t…

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## [Mass constraints for ApproxFun BVP system solver](https://discourse.julialang.org/t/mass-constraints-for-approxfun-bvp-system-solver/82257)

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**Author:** [@Jack\_hues](https://discourse.julialang.org/u/Jack_hues)\
**Replies:** 0\
**Last updated:** [June 5, 2022, 3:29am UTC](https://discourse.julialang.org/t/mass-constraints-for-approxfun-bvp-system-solver/82257 "2022-06-05T03:29:22Z")

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Does ApproxFun currently have a way to solve BVPs with mass conservation? For example 0=u''+f(u,v) and 0=v''-f(u,v) with homogeneous Neumann boundary conditions or periodic boundary conditions. Namely, can I tell ApproxF…

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## [Code running on local Julia, but failing on CI tests with Ububtu\_latest and Windows\_latest](https://discourse.julialang.org/t/code-running-on-local-julia-but-failing-on-ci-tests-with-ububtu-latest-and-windows-latest/80638)

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**Author:** [@andreasvarga](https://discourse.julialang.org/u/andreasvarga)\
**Replies:** 5\
**Last updated:** [May 8, 2022, 1:15pm UTC](https://discourse.julialang.org/t/code-running-on-local-julia-but-failing-on-ci-tests-with-ububtu-latest-and-windows-latest/80638 "2022-05-08T13:15:33Z")

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The following code is running correctly on my machine using LinearAlgebra using ApproxFun Af = Fun(t -\> \[0 1; -10\*cos(t) -24-10\*sin(t)\],Fourier(0..2π)); D = Derivative(domain(Af)); ND = \[D 0I; 0I D\]; Aop = Af - ND; NA =…

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## [Two questions related to using operators in ApproxFun.jl](https://discourse.julialang.org/t/two-questions-related-to-using-operators-in-approxfun-jl/79831)

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**Author:** [@andreasvarga](https://discourse.julialang.org/u/andreasvarga)\
**Replies:** 10\
**Last updated:** [April 30, 2022, 12:32pm UTC](https://discourse.julialang.org/t/two-questions-related-to-using-operators-in-approxfun-jl/79831 "2022-04-30T12:32:01Z")

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I am about to register PeriodicSystems.jl, a new package dedicated to handle linear control systems with periodic time-varying coefficient matrices. For stability analysis, the computation of characteristic exponents of …

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## [How to use ApproxFun to multiply differential operators without running into incompatible space issues?](https://discourse.julialang.org/t/how-to-use-approxfun-to-multiply-differential-operators-without-running-into-incompatible-space-issues/76481)

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**Author:** [@jishnub](https://discourse.julialang.org/u/jishnub)\
**Replies:** 2\
**Last updated:** [February 15, 2022, 12:54pm UTC](https://discourse.julialang.org/t/how-to-use-approxfun-to-multiply-differential-operators-without-running-into-incompatible-space-issues/76481 "2022-02-15T12:54:54Z")

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I’m trying to compute (D + x)^2, where D is the derivative operator. julia\> x = Fun(identity) Fun(Chebyshev(),\[0.0, 1.0\]) julia\> D = Derivative(Chebyshev()) ConcreteDerivative : Chebyshev() → Ultraspherical(1) ⋅ 1.0 …

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## [Chebfun equivalent for differentiation matrices in Julia?](https://discourse.julialang.org/t/chebfun-equivalent-for-differentiation-matrices-in-julia/74042)

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**Author:** [@yewalenikhil65](https://discourse.julialang.org/u/yewalenikhil65)\
**Replies:** 4\
**Last updated:** [January 4, 2022, 6:04pm UTC](https://discourse.julialang.org/t/chebfun-equivalent-for-differentiation-matrices-in-julia/74042 "2022-01-04T18:04:12Z")

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Is there yet a differentiation matrices calculating tool in some Julia package ? Something similar to https://github.com/chebfun/chebfun/blob/master/diffmat.m I have tried searching in JuliaApproximation community but c…