# Numerics

**URL:** https://discourse.julialang.org/c/domain/numerics/20.md?page=1

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**Page:** 2

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## [OrdinaryDiffEq with a mass\_matrix and jac\_prototype](https://discourse.julialang.org/t/ordinarydiffeq-with-a-mass-matrix-and-jac-prototype/134462)

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**Author:** [@bmxam](https://discourse.julialang.org/u/bmxam)\
**Replies:** 4\
**Last updated:** [December 10, 2025, 5:13pm UTC](https://discourse.julialang.org/t/ordinarydiffeq-with-a-mass-matrix-and-jac-prototype/134462 "2025-12-10T17:13:08Z")

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Hi everyone, Short story : see the MWE below. Using OrdinaryDiffEq, I’m trying to solve an ODE involving a mass\_matrix that (may) evolve depending on the solution, the time, the parameters. So I set up a SciMLOperators…

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## [Need help solving boundary value problem using SciML collocation, when I have unknown parameters in boundary conditions](https://discourse.julialang.org/t/need-help-solving-boundary-value-problem-using-sciml-collocation-when-i-have-unknown-parameters-in-boundary-conditions/134404)

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**Author:** [@ThermionicsGuy](https://discourse.julialang.org/u/ThermionicsGuy)\
**Replies:** 3\
**Last updated:** [December 8, 2025, 6:35pm UTC](https://discourse.julialang.org/t/need-help-solving-boundary-value-problem-using-sciml-collocation-when-i-have-unknown-parameters-in-boundary-conditions/134404 "2025-12-08T18:35:45Z")

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I have a nonlinear two-point boundary value problem consisting of five first-order differential equations. There are three boundary conditions at t=0 and two at t=1. Each boundary condition set also has one unknown param…

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## [How to extrapolate on non-uniform grid?](https://discourse.julialang.org/t/how-to-extrapolate-on-non-uniform-grid/134394)

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**Author:** [@raman\_kumar](https://discourse.julialang.org/u/raman_kumar)\
**Replies:** 3\
**Last updated:** [December 7, 2025, 7:03am UTC](https://discourse.julialang.org/t/how-to-extrapolate-on-non-uniform-grid/134394 "2025-12-07T07:03:55Z")

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How to interpolate(actually extrapolate later) Bp values on r,θand ϕ grid? I have non-uniform grid of r,θand ϕ, where r is geometric series and θand ϕ have constant spacing. r = Float32\[1.677044, 1.8385518, 2.0156136, 2…

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## [NonlinearSolve.jl : mimic SimpleNewtonRaphson with NewtonRaphson](https://discourse.julialang.org/t/nonlinearsolve-jl-mimic-simplenewtonraphson-with-newtonraphson/134280)

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**Author:** [@bmxam](https://discourse.julialang.org/u/bmxam)\
**Replies:** 5\
**Last updated:** [December 5, 2025, 2:50pm UTC](https://discourse.julialang.org/t/nonlinearsolve-jl-mimic-simplenewtonraphson-with-newtonraphson/134280 "2025-12-05T14:50:57Z")

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Hi everyone, I’m trying to solve a non-linear equation using a Newton-Raphson method using NonlinearSolve.jl . I have my own implementation of a basic Newton-Raphson algorithm, and the SimpleNewtonRaphson algorithm does…

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## [Is \`callback\` really compatible with NonlinearProblem?](https://discourse.julialang.org/t/is-callback-really-compatible-with-nonlinearproblem/134332)

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**Author:** [@bmxam](https://discourse.julialang.org/u/bmxam)\
**Replies:** 4\
**Last updated:** [December 5, 2025, 12:07pm UTC](https://discourse.julialang.org/t/is-callback-really-compatible-with-nonlinearproblem/134332 "2025-12-05T12:07:45Z")

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Hi everyone, According to the documentation (Nonlinear Problems · NonlinearSolve.jl), “if you set a callback in the problem, then that callback will be added in every solve call”. So I tried to add a callback but nothin…

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## [Seeking faster method for finding top eigenvalues of large dense matrices](https://discourse.julialang.org/t/seeking-faster-method-for-finding-top-eigenvalues-of-large-dense-matrices/134231)

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**Author:** [@Udonge](https://discourse.julialang.org/u/Udonge)\
**Replies:** 18\
**Last updated:** [December 4, 2025, 1:49pm UTC](https://discourse.julialang.org/t/seeking-faster-method-for-finding-top-eigenvalues-of-large-dense-matrices/134231 "2025-12-04T13:49:11Z")

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Hello everyone, I am new to the Julia language, and I’ve encountered a performance issue with an eigenvalue computation. Please feel free to point out any confusing statements or beginner mistakes! I need to compute th…

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## [Testing and tolerances for implicitly calculated functions and their AD](https://discourse.julialang.org/t/testing-and-tolerances-for-implicitly-calculated-functions-and-their-ad/133575)

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**Author:** [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Replies:** 3\
**Last updated:** [December 2, 2025, 12:49pm UTC](https://discourse.julialang.org/t/testing-and-tolerances-for-implicitly-calculated-functions-and-their-ad/133575 "2025-12-02T12:49:17Z")

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To fix ideas, suppose we have a function x = g(p) defined by f(x(p), p) = 0, both arguments are scalars. The numerical implementation involves finding an x such that | f(x, p)| \\le \\mathrm{tol}, either by Newton’s metho…

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## [Meshgrid function in Julia](https://discourse.julialang.org/t/meshgrid-function-in-julia/48679)

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**Author:** [@Hrishikesh\_Das](https://discourse.julialang.org/u/Hrishikesh_Das)\
**Replies:** 35\
**Last updated:** [November 27, 2025, 11:05am UTC](https://discourse.julialang.org/t/meshgrid-function-in-julia/48679 "2025-11-27T11:05:15Z")

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hello everyone I am new to Julia. Earlier I was using Matlab but now I have started to work in Julia. I would like to know is there any similar function available in julia like Meshgrid which is available in matlab. Plea…

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## [Cubic B spline, path generation in Julia and execution in C++](https://discourse.julialang.org/t/cubic-b-spline-path-generation-in-julia-and-execution-in-c/134020)

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**Author:** [@romain-chiap](https://discourse.julialang.org/u/romain-chiap)\
**Replies:** 0\
**Last updated:** [November 21, 2025, 9:47am UTC](https://discourse.julialang.org/t/cubic-b-spline-path-generation-in-julia-and-execution-in-c/134020 "2025-11-21T09:47:37Z")

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Hello, Given some data points tx, x. I would like to represent the path tx,x as well as its first and second derivative. I need my path to be C² continuous and small. It will be running in embedded C++ I have a set of …

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## [ForwardDiff.jl with FFTW.jl](https://discourse.julialang.org/t/forwarddiff-jl-with-fftw-jl/97366)

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**Author:** [@Bill\_Holmes](https://discourse.julialang.org/u/Bill_Holmes)\
**Replies:** 5\
**Last updated:** [November 14, 2025, 8:15am UTC](https://discourse.julialang.org/t/forwarddiff-jl-with-fftw-jl/97366 "2025-11-14T08:15:54Z")

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Hello all. I am working with ForwardDiff.jl on a problem that requires computing kernel density estimates (and thus convolutions which boils down to FFT). I am searching for a way to do this using autodifferentation. I r…

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## [Robust solver for ℝ³ → ℝ³ root with flat parts](https://discourse.julialang.org/t/robust-solver-for-root-with-flat-parts/133481)

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**Author:** [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Replies:** 5\
**Last updated:** [October 30, 2025, 2:40pm UTC](https://discourse.julialang.org/t/robust-solver-for-root-with-flat-parts/133481 "2025-10-30T14:40:21Z")

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I have an ℝ³ → ℝ³ function f which is differentiable (the computation uses an implicit solution, but I implemented the derivatives for Enzyme.jl, Mooncake.jl, and ForwardDiff.jl). I would like to find the root f(x) = 0. …

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## [Rem2pi(pi) errors](https://discourse.julialang.org/t/rem2pi-pi-errors/133010)

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**Author:** [@jerlich](https://discourse.julialang.org/u/jerlich)\
**Replies:** 0\
**Last updated:** [October 9, 2025, 1:42pm UTC](https://discourse.julialang.org/t/rem2pi-pi-errors/133010 "2025-10-09T13:42:49Z")

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There is a PR to fix, but it hasn’t been merged for 2 years.

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## [Differentiation of incomplete Beta function](https://discourse.julialang.org/t/differentiation-of-incomplete-beta-function/49675)

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**Author:** [@arzwa](https://discourse.julialang.org/u/arzwa)\
**Replies:** 4\
**Last updated:** [October 5, 2025, 12:55pm UTC](https://discourse.julialang.org/t/differentiation-of-incomplete-beta-function/49675 "2025-10-05T12:55:22Z")

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First, to give some context: my use case is equivalent to the following contrived example, in which I would like to define a (Turing.jl) probabilistic program that uses a discretized Beta mixture model. @model themodel(…

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## [Speeding up N-dimensional integration](https://discourse.julialang.org/t/speeding-up-n-dimensional-integration/132782)

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**Author:** [@owiecc](https://discourse.julialang.org/u/owiecc)\
**Replies:** 14\
**Last updated:** [October 1, 2025, 2:17pm UTC](https://discourse.julialang.org/t/speeding-up-n-dimensional-integration/132782 "2025-10-01T14:17:14Z")

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I am struggling to speed up a N-dimensional integration problem. To me it looks that allocations are the problem. I chased as many allocations I could find in the code but I still would like to speed-up the code by at le…

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## [Solving a non-linear P(I)DE - neural field equation](https://discourse.julialang.org/t/solving-a-non-linear-p-i-de-neural-field-equation/132678)

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**Author:** [@jucheval](https://discourse.julialang.org/u/jucheval)\
**Replies:** 3\
**Last updated:** [September 29, 2025, 8:53am UTC](https://discourse.julialang.org/t/solving-a-non-linear-p-i-de-neural-field-equation/132678 "2025-09-29T08:53:16Z")

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Hi everyone ! I am searching for some way to solve the following non linear P(I)DE, known as the neural field equation: \\frac{\\partial}{\\partial\_t} u(t,x) = -\\alpha u(t,x) + \\int w(y,x) f(u(t,y)) dy, for some scalar \\…

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## [Solving a non-linear P(I)DE - age-structured equation](https://discourse.julialang.org/t/solving-a-non-linear-p-i-de-age-structured-equation/132677)

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**Author:** [@jucheval](https://discourse.julialang.org/u/jucheval)\
**Replies:** 5\
**Last updated:** [September 29, 2025, 8:51am UTC](https://discourse.julialang.org/t/solving-a-non-linear-p-i-de-age-structured-equation/132677 "2025-09-29T08:51:02Z")

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Hi everyone ! I am searching for some way to solve the following non-linear P(I)DE, known as the refractory density equation or age-structured equation: \\begin{cases} \\frac{\\partial}{\\partial\_t} u(t,a) + \\frac{\\pa…

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## [Finding all zeros of a univariate function on the real line](https://discourse.julialang.org/t/finding-all-zeros-of-a-univariate-function-on-the-real-line/132565)

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**Author:** [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Replies:** 5\
**Last updated:** [September 26, 2025, 10:23pm UTC](https://discourse.julialang.org/t/finding-all-zeros-of-a-univariate-function-on-the-real-line/132565 "2025-09-26T22:23:51Z")

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I am trying to find all zeros of f(z) = C\_m + D\_m H(C\_f + D\_f H(z)) - z where C\_i, D\_i \\in \\mathbb{R} (can be any sign) and H is the CDF of the standard normal. If someone wants to experiment, this can be coded in Ju…

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## [Only trivial solution in BifurcationKit](https://discourse.julialang.org/t/only-trivial-solution-in-bifurcationkit/132391)

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**Author:** [@acubed](https://discourse.julialang.org/u/acubed)\
**Replies:** 13\
**Last updated:** [September 22, 2025, 9:09pm UTC](https://discourse.julialang.org/t/only-trivial-solution-in-bifurcationkit/132391 "2025-09-22T21:09:03Z")

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I try to investigate pitchfork bifurcation, using the BifurcationKit. My problem looks as follow. I start from some definitions: ND = 500 dx = 1.0/ND x = collect(1:ND)\*dx.-dx/2 J = +1.0 beta0 = 0.1 u0 = 0.01\*ones(Float…

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## [How to debug ODE model aborting midway on sensitivity computation](https://discourse.julialang.org/t/how-to-debug-ode-model-aborting-midway-on-sensitivity-computation/132096)

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**Author:** [@Neodym](https://discourse.julialang.org/u/Neodym)\
**Replies:** 9\
**Last updated:** [September 15, 2025, 9:25pm UTC](https://discourse.julialang.org/t/how-to-debug-ode-model-aborting-midway-on-sensitivity-computation/132096 "2025-09-15T21:25:06Z")

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Hi there, I have an ODE model that results from the spatial discretization of a PDE including reaction terms. The rate coefficient of the reaction is calculated from an interpolation that is provided externally. I can …

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## [Transform ODE Solution](https://discourse.julialang.org/t/transform-ode-solution/132262)

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**Author:** [@homocarbonis](https://discourse.julialang.org/u/homocarbonis)\
**Replies:** 5\
**Last updated:** [September 11, 2025, 8:37am UTC](https://discourse.julialang.org/t/transform-ode-solution/132262 "2025-09-11T08:37:16Z")

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Hi, I’m trying to solve some PDEs using a pseudo-spectral method with SplitODEProblem, which gives me a solution in the wavenumber domain. Is there a good way to take the inverse DCT of the solution, or am I going about…

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## [Autodifferentiation with FFT, with Enzyme?](https://discourse.julialang.org/t/autodifferentiation-with-fft-with-enzyme/128674)

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**Author:** [@jtravs](https://discourse.julialang.org/u/jtravs)\
**Replies:** 13\
**Last updated:** [September 9, 2025, 3:25pm UTC](https://discourse.julialang.org/t/autodifferentiation-with-fft-with-enzyme/128674 "2025-09-09T15:25:34Z")

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Hi, I’m trying to use autodifferentiation (for gradients, jacobians), working with a complex code that uses a lot of array mutation, custom structs, and FFTs (using FFTW). I got a small part of my code working by making…

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## [CUDSS adjoint factorization](https://discourse.julialang.org/t/cudss-adjoint-factorization/131841)

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**Author:** [@Gabrio\_Rizzuti](https://discourse.julialang.org/u/Gabrio_Rizzuti)\
**Replies:** 2\
**Last updated:** [September 3, 2025, 8:54pm UTC](https://discourse.julialang.org/t/cudss-adjoint-factorization/131841 "2025-09-03T20:54:13Z")

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Hello! My question is relatively straightforward. I’d like to use the LU factorization of the adjoint of a sparse matrix of type CuSparseMatrixCSR with the package CUDSS.jl, e.g. lu(A'), by only having access to lu(A). …

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## [NonlinearSolve.jl: Possible to store solution in-place of initial guess?](https://discourse.julialang.org/t/nonlinearsolve-jl-possible-to-store-solution-in-place-of-initial-guess/131208)

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**Author:** [@DanDoe](https://discourse.julialang.org/u/DanDoe)\
**Replies:** 16\
**Last updated:** [August 19, 2025, 7:23am UTC](https://discourse.julialang.org/t/nonlinearsolve-jl-possible-to-store-solution-in-place-of-initial-guess/131208 "2025-08-19T07:23:49Z")

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The standard workfllow to access the solution of a nonlinear\_eq = NonlinearProblem is something like sol = SciMLBase.solve(nonlinear\_eq, NewtonRaphson(autodiff = AutoFiniteDiff())); Is it possible to suppress the build…

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## [LDLt factorization for full matrices](https://discourse.julialang.org/t/ldlt-factorization-for-full-matrices/75356)

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**Author:** [@mancolric](https://discourse.julialang.org/u/mancolric)\
**Replies:** 27\
**Last updated:** [August 18, 2025, 10:16am UTC](https://discourse.julialang.org/t/ldlt-factorization-for-full-matrices/75356 "2025-08-18T10:16:10Z")

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Is there a way to compute the LDL^T factorization of a full matrix?? It seems that currently ldlt and LDLt support only SymTridiagonal and SparseMatrixCSC. However, lu works for full matrices. For example, using Linear…

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## [How to notify JuliaMath of a PR to one of their (almost) unwatched packages](https://discourse.julialang.org/t/how-to-notify-juliamath-of-a-pr-to-one-of-their-almost-unwatched-packages/131655)

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**Author:** [@PeterSimon](https://discourse.julialang.org/u/PeterSimon)\
**Replies:** 4\
**Last updated:** [August 18, 2025, 7:41am UTC](https://discourse.julialang.org/t/how-to-notify-juliamath-of-a-pr-to-one-of-their-almost-unwatched-packages/131655 "2025-08-18T07:41:23Z")

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I recently submitted a PR to FunctionZeros.jl to implement new functionality I need for a package I’m developing. FunctionZeros.jl is in the JuliaMath organization, and I’m not sure of the proper protocol, if any, to not…

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## [Different results when using 1 and 1.0 in expression](https://discourse.julialang.org/t/different-results-when-using-1-and-1-0-in-expression/131617)

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**Author:** [@jogama](https://discourse.julialang.org/u/jogama)\
**Replies:** 7\
**Last updated:** [August 14, 2025, 9:38pm UTC](https://discourse.julialang.org/t/different-results-when-using-1-and-1-0-in-expression/131617 "2025-08-14T21:38:19Z")

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d = (1+0im, 1.0+0im) (sqrt(exp(-d\[1\]) - 1), sqrt(exp(-d\[2\]) - 1)) (0.0 + 0.7950600976206501im, 0.0 - 0.7950600976206501im) also d = (1+0im, 1.0+0im); (sqrt(exp(-d\[1\]) - 1.0), …

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## [Can we solve complex valued two point boundary value problems?](https://discourse.julialang.org/t/can-we-solve-complex-valued-two-point-boundary-value-problems/53232)

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**Author:** [@406700](https://discourse.julialang.org/u/406700)\
**Replies:** 12\
**Last updated:** [August 13, 2025, 5:13pm UTC](https://discourse.julialang.org/t/can-we-solve-complex-valued-two-point-boundary-value-problems/53232 "2025-08-13T17:13:25Z")

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Hi, I am new to using Julia for differential equations. I am having a problem trying to solve a complex valued two point boundary value problem using the MIRK4 solver. I have tried to define complex valued initial condi…

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## [Solving linear system without allocating](https://discourse.julialang.org/t/solving-linear-system-without-allocating/130300)

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**Author:** [@freeman](https://discourse.julialang.org/u/freeman)\
**Replies:** 19\
**Last updated:** [August 9, 2025, 11:34pm UTC](https://discourse.julialang.org/t/solving-linear-system-without-allocating/130300 "2025-08-09T23:34:14Z")

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First off, this isn’t advanced stuff, conceptually it should be straightforward. I’m almost sure this is just me missing something basic. So I’m implementing an algorithm which is just a sequence of matrix multiplicatio…

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## [Pure-Julia Sparse Cholesky](https://discourse.julialang.org/t/pure-julia-sparse-cholesky/131293)

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**Author:** [@samuelsonric](https://discourse.julialang.org/u/samuelsonric)\
**Replies:** 31\
**Last updated:** [August 6, 2025, 10:01pm UTC](https://discourse.julialang.org/t/pure-julia-sparse-cholesky/131293 "2025-08-06T22:01:33Z")

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I implemented the Cholesky decomposition of sparse positive-definite matrices in CliqueTrees.jl. The implementation is pure-Julia, except for some calls to BLAS and LAPACK kernels. Even the column-ordering algorithm is w…

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## [Choosing suitable options for solver ODE](https://discourse.julialang.org/t/choosing-suitable-options-for-solver-ode/77843)

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**Author:** [@Camilo\_Chaparro](https://discourse.julialang.org/u/Camilo_Chaparro)\
**Replies:** 2\
**Last updated:** [August 6, 2025, 1:28pm UTC](https://discourse.julialang.org/t/choosing-suitable-options-for-solver-ode/77843 "2025-08-06T13:28:41Z")

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Hello everyone, I want about the most suitable ODE solver for the following problem: using DifferentialEquations using Plots; plotly() #Parameters omega\_m = 1.6e6 N = 1 Delta\_mw = -0.7 …

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