# Numerics

**URL:** https://discourse.julialang.org/c/domain/numerics/20.md

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## [About the Numerics category](https://discourse.julialang.org/t/about-the-numerics-category/283)

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**Author:** [@vchuravy](https://discourse.julialang.org/u/vchuravy)\
**Replies:** 0

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This subcategory is for discussion of Julia implementations of general methods for solving scientific and engineering problems. In particular, linear algebra differential equations quadrature interpolation special func…

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## [Running out of RAM with repeated cholesky solves](https://discourse.julialang.org/t/running-out-of-ram-with-repeated-cholesky-solves/136044)

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**Author:** [@falconflier](https://discourse.julialang.org/u/falconflier)\
**Replies:** 16\
**Last updated:** [September 3, 2026, 8:58am UTC](https://discourse.julialang.org/t/running-out-of-ram-with-repeated-cholesky-solves/136044 "2026-09-03T08:58:43Z")

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Hello, I have a system in which I need to repeatedly solve an electrostatics problem with an evolving charge configuration. When I left my program running overnight, I came back to find that RAM utilization had accumula…

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## [Space-time FEM for elastic wave propagation — no time stepping](https://discourse.julialang.org/t/space-time-fem-for-elastic-wave-propagation-no-time-stepping/138901)

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**Author:** [@perebalazs](https://discourse.julialang.org/u/perebalazs)\
**Replies:** 5\
**Last updated:** [August 20, 2026, 1:18pm UTC](https://discourse.julialang.org/t/space-time-fem-for-elastic-wave-propagation-no-time-stepping/138901 "2026-08-20T13:18:31Z")

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I have been experimenting with a simple space-time finite element formulation for 1D elastodynamics, and I thought the example might be interesting for the Numerics category. The problem is an elastic bar immediately af…

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## [MTK SDDE ArgumentError when Connecting two Components](https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861)

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**Author:** [@bebrunn](https://discourse.julialang.org/u/bebrunn)\
**Replies:** 7\
**Last updated:** [August 18, 2026, 11:38am UTC](https://discourse.julialang.org/t/mtk-sdde-argumenterror-when-connecting-two-components/138861 "2026-08-18T11:38:45Z")

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Hi, I am trying to connect two MTK components and then solve the resulting SDDE system. However, I am getting an ArgumentsError that I don’t understand. using ModelingToolkit using DifferentialEquations using ModelingT…

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## [Cg! per-iteration trace differs between single call and multiple calls](https://discourse.julialang.org/t/cg-per-iteration-trace-differs-between-single-call-and-multiple-calls/138408)

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**Author:** [@pitsianis](https://discourse.julialang.org/u/pitsianis)\
**Replies:** 6\
**Last updated:** [August 4, 2026, 7:29am UTC](https://discourse.julialang.org/t/cg-per-iteration-trace-differs-between-single-call-and-multiple-calls/138408 "2026-08-04T07:29:13Z")

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Calling IterativeSolvers.cg! for N iterations in one call produces a different per-iteration residual sequence than performing the same total number of iterations via multiple cg! calls. A single call with 6 iterations …

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## [Package For Constructing Finite Difference Operators on Non-Uniform Grid?](https://discourse.julialang.org/t/package-for-constructing-finite-difference-operators-on-non-uniform-grid/138333)

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**Author:** [@ducksoverip](https://discourse.julialang.org/u/ducksoverip)\
**Replies:** 11\
**Last updated:** [July 22, 2026, 11:35am UTC](https://discourse.julialang.org/t/package-for-constructing-finite-difference-operators-on-non-uniform-grid/138333 "2026-07-22T11:35:43Z")

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In my efforts to write a Julia program that solves the time-dependent Schrodinger equation for helium, I’ve gotten as far as solving the time-independent case for the ground state, with some much-appreciated help from @k…

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## [What can mathematics graduate student do to help out?](https://discourse.julialang.org/t/what-can-mathematics-graduate-student-do-to-help-out/138118)

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**Author:** [@Alex-Scofield](https://discourse.julialang.org/u/Alex-Scofield)\
**Replies:** 4\
**Last updated:** [July 12, 2026, 8:49pm UTC](https://discourse.julialang.org/t/what-can-mathematics-graduate-student-do-to-help-out/138118 "2026-07-12T20:49:43Z")

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I am a student enrolled in a master’s degree in analysis, modelling and simulations. I have already followed a couple of introduction courses on these subjects, and completed a degree in pure mathematics and computer sci…

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## [Interpolating solution to constrained BVP](https://discourse.julialang.org/t/interpolating-solution-to-constrained-bvp/137989)

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**Author:** [@kar15](https://discourse.julialang.org/u/kar15)\
**Replies:** 3\
**Last updated:** [July 9, 2026, 7:41am UTC](https://discourse.julialang.org/t/interpolating-solution-to-constrained-bvp/137989 "2026-07-09T07:41:02Z")

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Hi all! When trying to find interpolated values of a solution to a constrained BVP using SciMLs collocation method, I get an error. Here is a MWE: using BoundaryValueDiffEq, OptimizationIpopt function f!(du, u, p, t) …

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## [Is there a general guide to Julia's PDE solving utilities based on the properties of the PDE in question?](https://discourse.julialang.org/t/is-there-a-general-guide-to-julias-pde-solving-utilities-based-on-the-properties-of-the-pde-in-question/137545)

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**Author:** [@ducksoverip](https://discourse.julialang.org/u/ducksoverip)\
**Replies:** 2\
**Last updated:** [June 10, 2026, 7:30pm UTC](https://discourse.julialang.org/t/is-there-a-general-guide-to-julias-pde-solving-utilities-based-on-the-properties-of-the-pde-in-question/137545 "2026-06-10T19:30:56Z")

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As I continue my foray into Julia, I’d like to apply it more directly to my research by utilizing its PDE-solving capabilities to solve the radial Schrodinger equation for one and two-electron systems, with an eye toward…

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## [Fuzzy Logic for Verifying Numerical Order of a Method](https://discourse.julialang.org/t/fuzzy-logic-for-verifying-numerical-order-of-a-method/137385)

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**Author:** [@leespen1](https://discourse.julialang.org/u/leespen1)\
**Replies:** 6\
**Last updated:** [June 3, 2026, 12:53am UTC](https://discourse.julialang.org/t/fuzzy-logic-for-verifying-numerical-order-of-a-method/137385 "2026-06-03T00:53:08Z")

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I often program numerical methods for solving initial value problems, and would like to test their order of convergence. However, I find that it is difficult to have automated convergence tests, due to the pre-asymptotic…

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## [Creating a macro to call @tullio with arbitrary dimensions](https://discourse.julialang.org/t/creating-a-macro-to-call-tullio-with-arbitrary-dimensions/135848)

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**Author:** [@nicrummel](https://discourse.julialang.org/u/nicrummel)\
**Replies:** 2\
**Last updated:** [April 20, 2026, 11:21am UTC](https://discourse.julialang.org/t/creating-a-macro-to-call-tullio-with-arbitrary-dimensions/135848 "2026-04-20T11:21:27Z")

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Hello everyone, Custom Macro I am hoping to be able to write a macro that can call @tullio to specify an arbitrary sized linear form. I think this should follow from some easy-ish fix similar to an old thread… but I am …

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## [SciML collocation BVP solvers overwrite the initial guess - bug or feature?](https://discourse.julialang.org/t/sciml-collocation-bvp-solvers-overwrite-the-initial-guess-bug-or-feature/136715)

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**Author:** [@ThermionicsGuy](https://discourse.julialang.org/u/ThermionicsGuy)\
**Replies:** 6\
**Last updated:** [April 16, 2026, 4:36pm UTC](https://discourse.julialang.org/t/sciml-collocation-bvp-solvers-overwrite-the-initial-guess-bug-or-feature/136715 "2026-04-16T16:36:37Z")

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I’ve encountered a behavior that I didn’t expect when solving BVPs with SciML collocation methods and using the continuation method. When you call “solve” and are using a previous solution object as the initial guess, th…

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## [Package for generalized special functions](https://discourse.julialang.org/t/package-for-generalized-special-functions/67076)

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**Author:** [@amrods](https://discourse.julialang.org/u/amrods)\
**Replies:** 1\
**Last updated:** [April 5, 2026, 9:00pm UTC](https://discourse.julialang.org/t/package-for-generalized-special-functions/67076 "2026-04-05T21:00:57Z")

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Is there any package that implements “generalized” special functions like the Meijer G-function, Fox–Wright Psi-function, Fox H-function? My go to for this kind of needs GSL.jl doesn’t have them.

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## [ApproxFun: Eigenvalue Problem for Linear Differential Algebraic Equations](https://discourse.julialang.org/t/approxfun-eigenvalue-problem-for-linear-differential-algebraic-equations/136369)

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**Author:** [@RayleighLord](https://discourse.julialang.org/u/RayleighLord)\
**Replies:** 7\
**Last updated:** [March 25, 2026, 7:41pm UTC](https://discourse.julialang.org/t/approxfun-eigenvalue-problem-for-linear-differential-algebraic-equations/136369 "2026-03-25T19:41:26Z")

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I want to ask for help and guidance to know if the following problem can be solved using ApproxFun, as I have not encountered any example doing a similar thing. Consider, for instance, a linear system of differential al…

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## [Custom rule for an implicit function in Enzyme](https://discourse.julialang.org/t/custom-rule-for-an-implicit-function-in-enzyme/136259)

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**Author:** [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Replies:** 3\
**Last updated:** [March 25, 2026, 12:01pm UTC](https://discourse.julialang.org/t/custom-rule-for-an-implicit-function-in-enzyme/136259 "2026-03-25T12:01:04Z")

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Consider an implicit function y = f(x) defined via g(x, y) where x, y \\in \\mathbb{R}^n. The user supplies f!(y, x) and g!(r, x, y) as callables, which are wrapped in a struct SquareImplicitFunction{F,G} f!::F …

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## [SciML FIRK BVP solvers don't pass initial guess to boundary conditions correctly](https://discourse.julialang.org/t/sciml-firk-bvp-solvers-dont-pass-initial-guess-to-boundary-conditions-correctly/136324)

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**Author:** [@ThermionicsGuy](https://discourse.julialang.org/u/ThermionicsGuy)\
**Replies:** 4\
**Last updated:** [March 23, 2026, 10:54pm UTC](https://discourse.julialang.org/t/sciml-firk-bvp-solvers-dont-pass-initial-guess-to-boundary-conditions-correctly/136324 "2026-03-23T22:54:44Z")

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I have a complex non-linear two-point boundary value problem to solve. It’s very sensitive to how close the initial guess is to the final converged answer. I start by solving in a region where convergence is easier, then…

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## [Defining a preconditioner for IterativeSolvers](https://discourse.julialang.org/t/defining-a-preconditioner-for-iterativesolvers/86977)

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**Author:** [@Gravlax](https://discourse.julialang.org/u/Gravlax)\
**Replies:** 18\
**Last updated:** [March 20, 2026, 3:10pm UTC](https://discourse.julialang.org/t/defining-a-preconditioner-for-iterativesolvers/86977 "2026-03-20T15:10:30Z")

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Dear all, I would like to solve a linear(ised) system of equations using IterativeSolvers, however I am not sure how to define the preconditioner. The preconditonner is a symmetric positive-definite sparse matrix and t…

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## [Has the nested\_nlsolve\_kwargs keyword been removed from the SciML FIRK BVP solvers?](https://discourse.julialang.org/t/has-the-nested-nlsolve-kwargs-keyword-been-removed-from-the-sciml-firk-bvp-solvers/135934)

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**Author:** [@ThermionicsGuy](https://discourse.julialang.org/u/ThermionicsGuy)\
**Replies:** 3\
**Last updated:** [March 1, 2026, 5:41pm UTC](https://discourse.julialang.org/t/has-the-nested-nlsolve-kwargs-keyword-been-removed-from-the-sciml-firk-bvp-solvers/135934 "2026-03-01T17:41:44Z")

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I want to control the tolerances and choice of nonlinear solution algorithm in the nested solver for the RaduaIIa5 boundary value problem solver. The documentation I can find says to use the nested\_nlsolve\_kwargs keyword…

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## [A non-classical ODE problem](https://discourse.julialang.org/t/a-non-classical-ode-problem/135868)

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**Author:** [@Veenty](https://discourse.julialang.org/u/Veenty)\
**Replies:** 2\
**Last updated:** [February 26, 2026, 5:03pm UTC](https://discourse.julialang.org/t/a-non-classical-ode-problem/135868 "2026-02-26T17:03:03Z")

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I have an evolution problem that I cannot cast in a classical form. \\frac{d}{dt} A u = u + F(u,v) \\\\ G(u) = 0 Where A is a bad matrix to invert, however (A - \\Delta t) is ok to invert. When I’m coding this with an imp…

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## [Automatic Differentiation of the flow of an ode : DifferentiationInterface, SciMLSensitivity](https://discourse.julialang.org/t/automatic-differentiation-of-the-flow-of-an-ode-differentiationinterface-scimlsensitivity/135730)

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**Author:** [@joseph-gergaud](https://discourse.julialang.org/u/joseph-gergaud)\
**Replies:** 1\
**Last updated:** [February 20, 2026, 6:23am UTC](https://discourse.julialang.org/t/automatic-differentiation-of-the-flow-of-an-ode-differentiationinterface-scimlsensitivity/135730 "2026-02-20T06:23:04Z")

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When I use the backend Zygote for the automatic differentiation with DifferentiationInterface for the flow of an ordinary differentiation equation, I have an error : Here is the code : using Pkg Pkg.activate(".") #Pkg.…

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## [On a minimalistic interface for DifferentialEquations.jl](https://discourse.julialang.org/t/on-a-minimalistic-interface-for-differentialequations-jl/135575)

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**Author:** [@Bizzi](https://discourse.julialang.org/u/Bizzi)\
**Replies:** 3\
**Last updated:** [February 12, 2026, 1:48pm UTC](https://discourse.julialang.org/t/on-a-minimalistic-interface-for-differentialequations-jl/135575 "2026-02-12T13:48:24Z")

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I, like most people here, think that DifferentialEquations.jl is a truly fantastic package and one of the major reasons to use Julia over other langs. Still, I’ve found that it is often very bulky: instead of returning a…

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## [Floating-point accuracy visualization example: the ULP error for each math function coming with Julia](https://discourse.julialang.org/t/floating-point-accuracy-visualization-example-the-ulp-error-for-each-math-function-coming-with-julia/135392)

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**Author:** [@nsajko](https://discourse.julialang.org/u/nsajko)\
**Replies:** 20\
**Last updated:** [February 6, 2026, 2:25pm UTC](https://discourse.julialang.org/t/floating-point-accuracy-visualization-example-the-ulp-error-for-each-math-function-coming-with-julia/135392 "2026-02-06T14:25:29Z")

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Introduction The implementation of a math function, such as cos(::Float64) in Julia, should be fast, but also needs to be at least somewhat accurate. Here I propose a method for visualizing empirical accuracy data. Cons…

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## [Help with setting up coupled PDE system for adsorption column](https://discourse.julialang.org/t/help-with-setting-up-coupled-pde-system-for-adsorption-column/130751)

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**Author:** [@shisac](https://discourse.julialang.org/u/shisac)\
**Replies:** 9\
**Last updated:** [February 4, 2026, 7:53am UTC](https://discourse.julialang.org/t/help-with-setting-up-coupled-pde-system-for-adsorption-column/130751 "2026-02-04T07:53:19Z")

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Hi all, I’m trying to model an adsorption column with a system of PDEs, which have been discretized in space using a WENO finite volume scheme. I’m new to julia and this is my first time simulating a complex system like…

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## [Parameter sensitivity of ODE with parameter-dependent event](https://discourse.julialang.org/t/parameter-sensitivity-of-ode-with-parameter-dependent-event/103602)

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**Author:** [@Neodym](https://discourse.julialang.org/u/Neodym)\
**Replies:** 4\
**Last updated:** [February 2, 2026, 11:28am UTC](https://discourse.julialang.org/t/parameter-sensitivity-of-ode-with-parameter-dependent-event/103602 "2026-02-02T11:28:17Z")

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Hey, I’m trying to get parameter sensitivities of an ODE problem with a parameter-dependent time-event. Just throwing AD at the problem doesn’t seem to work: using OrdinaryDiffEq using SciMLSensitivity using ForwardDi…

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## [Paper on the accuracy of math functions](https://discourse.julialang.org/t/paper-on-the-accuracy-of-math-functions/132227)

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**Author:** [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)\
**Replies:** 1\
**Last updated:** [February 1, 2026, 9:04pm UTC](https://discourse.julialang.org/t/paper-on-the-accuracy-of-math-functions/132227 "2026-02-01T21:04:20Z")

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Mantas Mikaitis and Tejaswa Rizyal have this well developed, reliable paper The software is available on github:

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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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## [Iterating over integer simplex](https://discourse.julialang.org/t/iterating-over-integer-simplex/135060)

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**Author:** [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Replies:** 14\
**Last updated:** [January 16, 2026, 12:29pm UTC](https://discourse.julialang.org/t/iterating-over-integer-simplex/135060 "2026-01-16T12:29:59Z")

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I need to iterate over all K-tuples of nonnegative Ints that sum to N. Eg if K is 3 and N==3, (0,0,3) (0,1,2) (0,2,1) (0,3,0) (1,0,2) (1,1,1) (1,2,0) (2,0,1) (2,1,0) (3,0,0) Ordering does not matter, just full travers…

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## [ParallelStencil Question](https://discourse.julialang.org/t/parallelstencil-question/134915)

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**Author:** [@ziolai](https://discourse.julialang.org/u/ziolai)\
**Replies:** 2\
**Last updated:** [January 6, 2026, 7:48pm UTC](https://discourse.julialang.org/t/parallelstencil-question/134915 "2026-01-06T19:48:22Z")

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Does ParallelStencil.jl support staggered grid implementations?

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## [Stochastic filtration problem](https://discourse.julialang.org/t/stochastic-filtration-problem/134713)

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**Author:** [@ymuv1](https://discourse.julialang.org/u/ymuv1)\
**Replies:** 1\
**Last updated:** [December 23, 2025, 7:13pm UTC](https://discourse.julialang.org/t/stochastic-filtration-problem/134713 "2025-12-23T19:13:46Z")

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Hi all, I’m working with a physical system whose state u(t) follows an SDE du=f(u,t)dt+g(u,t)dW\_t The system produces a measured signal Y\_t given by dY\_t = h(u,t)dt+dW\_t where dW\_t is the same Wiener increment in bo…

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## [Eigenvectors with the most overlap with v](https://discourse.julialang.org/t/eigenvectors-with-the-most-overlap-with-v/134008)

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**Author:** [@Nichola](https://discourse.julialang.org/u/Nichola)\
**Replies:** 7\
**Last updated:** [December 18, 2025, 1:39am UTC](https://discourse.julialang.org/t/eigenvectors-with-the-most-overlap-with-v/134008 "2025-12-18T01:39:40Z")

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Given a sparse matrix M and a vector v, I would like to get the k eigenvectors of M that have the most overlap with v. Is there an efficient method for doing this with sparse matrices ? All sparse solvers I ran into tar…

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