Sigmoid Social

mindsetsOn Pi Day 2025, as you might recall, I introduced you (more or less) to 3Blue1Brown. Also known as Grant Sanderson.If there's any better source of animated math presentations, than Mr. Sanderson, I'm unaware of it.Key word: "animated." In addition, he is a warm, enthusiastic teacher. And of course he knows his stuff well—how else could he have made the truly fantastic animations?I haven't watched them all yet. But so far, I especially like 2016's BUT WHAT IS THE RIEMANN ZETA FUNCTION? VISUALIZING ANALYTIC CONTINUATION and 2019's DIFFERENTIAL EQUATIONS, A TOURIST'S GUIDE | DE1.I may never again be able to ponder some ideas they convey, without seeing those animations in my head. They're that perfect.So give those two videos a try, if you're comfortable enough with the one I had shared on Pi Day...if now you want a couple which are more challenging. Maybe unforgettable, too.<a href="https://mindly.social/tags/3Blue1Brown" class="mention hashtag" rel="nofollow noopener" target="_blank">#3Blue1Brown</a> <a href="https://mindly.social/tags/RiemannZetaFunction" class="mention hashtag" rel="nofollow noopener" target="_blank">#RiemannZetaFunction</a> <a href="https://mindly.social/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#DifferentialEquations</a> <a href="https://mindly.social/tags/learning" class="mention hashtag" rel="nofollow noopener" target="_blank">#learning</a><a href="https://mindly.social/@setsly/114161481212443838" rel="nofollow noopener" translate="no" target="_blank">https://mindly.social/@setsly/114161481212443838</a><a href="https://www.youtube.com/watch?v=sD0NjbwqlYw" rel="nofollow noopener" translate="no" target="_blank">https://www.youtube.com/watch?v=sD0NjbwqlYw</a><a href="https://www.youtube.com/watch?v=p_di4Zn4wz4" rel="nofollow noopener" translate="no" target="_blank">https://www.youtube.com/watch?v=p_di4Zn4wz4</a>

Pustam | पुस्तम | পুস্তম🇳🇵A cycloidal pendulum - one suspended from the cusp of an inverted cycloid - is isochronous, meaning its period is constant regardless of the amplitude of the swing. Please find the proof using energy methods: Lagrange's equations (in the images attached to the reply).Background: The standard pendulum period of \(2\pi\sqrt{L/g}\) or frequency \(\sqrt{g/L}\) holds only for small oscillations. The frequency becomes smaller as the amplitude grows. If you want to build a pendulum whose frequency is independent of the amplitude, you should hang it from the cusp of a cycloid of a certain size, as shown in the gif. As the string wraps partially around the cycloid, the effect decreases the length of the string in the air, increasing the frequency back up to a constant value.In more detail: A cycloid is the path taken by a point on the rim of a rolling wheel. The upside-down cycloid in the gif can be parameterized by \((x, y)=R(\theta-\sin\theta, -1+\cos\theta)\), where \(\theta=0\) corresponds to the cusp. Consider a pendulum of length \(L=4R\) hanging from the cusp, and let \(\alpha\) be the angle the string makes with the vertical, as shown (in the proof).<a href="https://mathstodon.xyz/tags/Pendulum" class="mention hashtag" rel="nofollow noopener" target="_blank">#Pendulum</a> <a href="https://mathstodon.xyz/tags/Cycloid" class="mention hashtag" rel="nofollow noopener" target="_blank">#Cycloid</a> <a href="https://mathstodon.xyz/tags/Period" class="mention hashtag" rel="nofollow noopener" target="_blank">#Period</a> <a href="https://mathstodon.xyz/tags/Frequency" class="mention hashtag" rel="nofollow noopener" target="_blank">#Frequency</a> <a href="https://mathstodon.xyz/tags/SHM" class="mention hashtag" rel="nofollow noopener" target="_blank">#SHM</a> <a href="https://mathstodon.xyz/tags/TimePeriod" class="mention hashtag" rel="nofollow noopener" target="_blank">#TimePeriod</a> <a href="https://mathstodon.xyz/tags/CycloidalPendulum" class="mention hashtag" rel="nofollow noopener" target="_blank">#CycloidalPendulum</a> <a href="https://mathstodon.xyz/tags/Lagrange" class="mention hashtag" rel="nofollow noopener" target="_blank">#Lagrange</a> <a href="https://mathstodon.xyz/tags/Cusp" class="mention hashtag" rel="nofollow noopener" target="_blank">#Cusp</a> <a href="https://mathstodon.xyz/tags/Energy" class="mention hashtag" rel="nofollow noopener" target="_blank">#Energy</a> <a href="https://mathstodon.xyz/tags/KineticEnergy" class="mention hashtag" rel="nofollow noopener" target="_blank">#KineticEnergy</a> <a href="https://mathstodon.xyz/tags/PotentialEnergy" class="mention hashtag" rel="nofollow noopener" target="_blank">#PotentialEnergy</a> <a href="https://mathstodon.xyz/tags/Lagrangian" class="mention hashtag" rel="nofollow noopener" target="_blank">#Lagrangian</a> <a href="https://mathstodon.xyz/tags/Length" class="mention hashtag" rel="nofollow noopener" target="_blank">#Length</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#Maths</a> <a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Physics</a> <a href="https://mathstodon.xyz/tags/Mechanics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mechanics</a> <a href="https://mathstodon.xyz/tags/ClassicalMechanics" class="mention hashtag" rel="nofollow noopener" target="_blank">#ClassicalMechanics</a> <a href="https://mathstodon.xyz/tags/Amplitude" class="mention hashtag" rel="nofollow noopener" target="_blank">#Amplitude</a> <a href="https://mathstodon.xyz/tags/CircularFrequency" class="mention hashtag" rel="nofollow noopener" target="_blank">#CircularFrequency</a> <a href="https://mathstodon.xyz/tags/Motion" class="mention hashtag" rel="nofollow noopener" target="_blank">#Motion</a> <a href="https://mathstodon.xyz/tags/Vibration" class="mention hashtag" rel="nofollow noopener" target="_blank">#Vibration</a> <a href="https://mathstodon.xyz/tags/HarmonicMotion" class="mention hashtag" rel="nofollow noopener" target="_blank">#HarmonicMotion</a> <a href="https://mathstodon.xyz/tags/Parameter" class="mention hashtag" rel="nofollow noopener" target="_blank">#Parameter</a> <a href="https://mathstodon.xyz/tags/ParemeterizedEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#ParemeterizedEquation</a> <a href="https://mathstodon.xyz/tags/GoverningEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#GoverningEquations</a> <a href="https://mathstodon.xyz/tags/Equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Equation</a> <a href="https://mathstodon.xyz/tags/Equations" class="mention hashtag" rel="nofollow noopener" target="_blank">#Equations</a> <a href="https://mathstodon.xyz/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#DifferentialEquations</a> <a href="https://mathstodon.xyz/tags/Calculus" class="mention hashtag" rel="nofollow noopener" target="_blank">#Calculus</a>

Stefan Wolfrum :mastodon:I could watch forever ... <a href="https://mastodon.social/tags/LorenzAttractor" class="mention hashtag" rel="nofollow noopener" target="_blank">#LorenzAttractor</a> <a href="https://mastodon.social/tags/ButterflyEffect" class="mention hashtag" rel="nofollow noopener" target="_blank">#ButterflyEffect</a> <a href="https://mastodon.social/tags/JavaScript" class="mention hashtag" rel="nofollow noopener" target="_blank">#JavaScript</a> <a href="https://mastodon.social/tags/p5js" class="mention hashtag" rel="nofollow noopener" target="_blank">#p5js</a> <a href="https://mastodon.social/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#DifferentialEquations</a> <a href="https://mastodon.social/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mastodon.social/tags/visualization" class="mention hashtag" rel="nofollow noopener" target="_blank">#visualization</a> <a href="https://mastodon.social/tags/computergraphics" class="mention hashtag" rel="nofollow noopener" target="_blank">#computergraphics</a> <a href="https://mastodon.social/tags/dynamicsystems" class="mention hashtag" rel="nofollow noopener" target="_blank">#dynamicsystems</a>

Brain Dynamics ToolboxFinal call for the Modellers Workshop for the <a href="https://mastodon.au/tags/BrainDynamicsToolbox" class="mention hashtag" rel="nofollow noopener" target="_blank">#BrainDynamicsToolbox</a>. An online course for simulating custom <a href="https://mastodon.au/tags/DynamicalSystems" class="mention hashtag" rel="nofollow noopener" target="_blank">#DynamicalSystems</a> in <a href="https://mastodon.au/tags/Neuroscience" class="mention hashtag" rel="nofollow noopener" target="_blank">#Neuroscience</a>. It covers practical programming techniques for the major classes of <a href="https://mastodon.au/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#DifferentialEquations</a> in <a href="https://mastodon.au/tags/ComputationalNeuroscience" class="mention hashtag" rel="nofollow noopener" target="_blank">#ComputationalNeuroscience</a>. Example code is provided in all cases. Study time is 8 hours. Course Website <a href="https://bdtoolbox.teachable.com/p/modellers-workshop" rel="nofollow noopener" translate="no" target="_blank">https://bdtoolbox.teachable.com/p/modellers-workshop</a>Toolbox Website <a href="https://bdtoolbox.org" rel="nofollow noopener" translate="no" target="_blank">https://bdtoolbox.org</a>Important Dates Enrolments close 31st Aug 2024.

Brain Dynamics ToolboxEnrolments are now open for the Modellers Workshop for the <a href="https://mastodon.au/tags/BrainDynamicsToolbox" class="mention hashtag" rel="nofollow noopener" target="_blank">#BrainDynamicsToolbox</a>. This is an online course for researchers who wish to build custom <a href="https://mastodon.au/tags/DynamicalModels" class="mention hashtag" rel="nofollow noopener" target="_blank">#DynamicalModels</a> using the Brain Dynamics Toolbox. The course focuses on practical programming techniques for the major classes of <a href="https://mastodon.au/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#DifferentialEquations</a> (ordinary, partial, delay, stochastic) in <a href="https://mastodon.au/tags/ComputationalNeuroscience" class="mention hashtag" rel="nofollow noopener" target="_blank">#ComputationalNeuroscience</a>. Example code is provided in all cases. Study time is 8 hours. Upon completion, students will be able to turn differential equations into working simulations.Course Website <a href="https://bdtoolbox.teachable.com/p/modellers-workshop" rel="nofollow noopener" translate="no" target="_blank">https://bdtoolbox.teachable.com/p/modellers-workshop</a>Toolbox Website <a href="https://bdtoolbox.org" rel="nofollow noopener" translate="no" target="_blank">https://bdtoolbox.org</a>Important Dates Enrolments close 31st Aug 2024.

katch wrecki wonder if it's possible to make a video game that would teach kids the intuition behind the "butterfly effect" by making each subsequent level's initial conditions determined by the outcome of the previous level, in such a way that the gameplay would guide you towards understanding that tiny decisions made on the first level will have huge consequences on level two, etc. <a href="https://mastodon.social/tags/chaos" class="mention hashtag" rel="nofollow noopener" target="_blank">#chaos</a> <a href="https://mastodon.social/tags/butterflyEffect" class="mention hashtag" rel="nofollow noopener" target="_blank">#butterflyEffect</a> <a href="https://mastodon.social/tags/chaosTheory" class="mention hashtag" rel="nofollow noopener" target="_blank">#chaosTheory</a> <a href="https://mastodon.social/tags/deterministic" class="mention hashtag" rel="nofollow noopener" target="_blank">#deterministic</a> <a href="https://mastodon.social/tags/systems" class="mention hashtag" rel="nofollow noopener" target="_blank">#systems</a> <a href="https://mastodon.social/tags/nonlinear" class="mention hashtag" rel="nofollow noopener" target="_blank">#nonlinear</a> <a href="https://mastodon.social/tags/differentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#differentialEquations</a> <a href="https://mastodon.social/tags/bifurcation" class="mention hashtag" rel="nofollow noopener" target="_blank">#bifurcation</a> cc <a href="https://zirk.us/@JamesGleick" class="u-url mention" rel="nofollow noopener" target="_blank">@JamesGleick</a>

Pustam | पुस्तम | পুস্তম🇳🇵Convection–diffusion equation The convection-diffusion equation is a more general version of the scalar transport equation. It is a combination of the diffusion and convection (advection) equations. It describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. \[\dfrac{\partial c}{\partial t} = \mathbf{\nabla} \cdot (D \mathbf{\nabla} c - \mathbf{v} c) + R\]\[\dfrac{\partial c}{\partial t} = \underbrace{\mathbf{\nabla} \cdot (D \mathbf{\nabla} c)}_{\text{diffusion}}-\overbrace{\underbrace{\mathbf{\nabla}\cdot (\mathbf{v} c)}_{\text{advection}}}^\text{convection} + \overbrace{\underbrace{R}_\text{destruction}}^\text{creation}\] \(\mathbf{\nabla} \cdot (D \mathbf{\nabla} c)\) is the contribution of diffusion. \(- \mathbf{\nabla}\cdot (\mathbf{v} c)\) is the contribution of convection or advection. \(R\) describes the creation or destruction of the quantity.where \(c\) is the variable of interest. \(D\) is the diffusivity. \(\mathbf{v}\) is the velocity field, and \(R\) is the sources or sinks of the quantity \(c\).<a href="https://mathstodon.xyz/tags/Convection" class="mention hashtag" rel="nofollow noopener" target="_blank">#Convection</a> <a href="https://mathstodon.xyz/tags/Diffusion" class="mention hashtag" rel="nofollow noopener" target="_blank">#Diffusion</a> <a href="https://mathstodon.xyz/tags/Transport" class="mention hashtag" rel="nofollow noopener" target="_blank">#Transport</a> <a href="https://mathstodon.xyz/tags/Advection" class="mention hashtag" rel="nofollow noopener" target="_blank">#Advection</a> <a href="https://mathstodon.xyz/tags/Equation" class="mention hashtag" rel="nofollow noopener" target="_blank">#Equation</a> <a href="https://mathstodon.xyz/tags/ConvectionDiffusionEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#ConvectionDiffusionEquation</a> <a href="https://mathstodon.xyz/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#DifferentialEquations</a> <a href="https://mathstodon.xyz/tags/AdvectionEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#AdvectionEquation</a> <a href="https://mathstodon.xyz/tags/DiffusionEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#DiffusionEquation</a> <a href="https://mathstodon.xyz/tags/TransportEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#TransportEquation</a> <a href="https://mathstodon.xyz/tags/ConvectionEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#ConvectionEquation</a>

Jiri LeblA new lecture on undergraduate differential equations:17. Mechanical vibrations, part 1: free undamped motion (Notes on Diffy Qs, 2.4) <a href="https://youtu.be/RYti_vJ8sQU" rel="nofollow noopener" translate="no" target="_blank">https://youtu.be/RYti_vJ8sQU</a>Based on the free book: Notes on Diffy Qs <a href="https://www.jirka.org/diffyqs" rel="nofollow noopener" translate="no" target="_blank">https://www.jirka.org/diffyqs</a>The entire playlist is at: <a href="https://www.youtube.com/playlist?list=PLRfQb6m35rf5E7QllafnyOXD0tHHI_N9E" rel="nofollow noopener" translate="no" target="_blank">https://www.youtube.com/playlist?list=PLRfQb6m35rf5E7QllafnyOXD0tHHI_N9E</a><a href="https://mastodon.online/tags/math" class="mention hashtag" rel="nofollow noopener" target="_blank">#math</a> <a href="https://mastodon.online/tags/maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#maths</a> <a href="https://mastodon.online/tags/mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#mathematics</a> <a href="https://mastodon.online/tags/differentialequations" class="mention hashtag" rel="nofollow noopener" target="_blank">#differentialequations</a> <a href="https://mastodon.online/tags/diffyqs" class="mention hashtag" rel="nofollow noopener" target="_blank">#diffyqs</a> <a href="https://mastodon.online/tags/OER" class="mention hashtag" rel="nofollow noopener" target="_blank">#OER</a>

Joana de Castro ArnaudWhenever I walk to/from home, I have to walk up/down an inclined street; I noticed that the asphalt floor has different curvatures depending on how near it is of a bend, and I try to find a less steep incline while walking.This got me inspiration for the few questions below. Any simple explanations, and related links, are welcome.Given a <a href="https://mathstodon.xyz/tags/differentiable" class="mention hashtag" rel="nofollow noopener" target="_blank">#differentiable</a> surface within R^3, and two distinct points in it, there are infinitely many differentiable paths from one point to another, remaining on the surface. At each point of the <a href="https://mathstodon.xyz/tags/path" class="mention hashtag" rel="nofollow noopener" target="_blank">#path</a>, one can find the path's local <a href="https://mathstodon.xyz/tags/curvature" class="mention hashtag" rel="nofollow noopener" target="_blank">#curvature</a>. Then:- Find a path that minimizes the supreme of the curvature. In other words, find the "flattest" path.- Find a path that minimizes the variation of the curvature. In other words, find a path that "most resembles" a circle arc.Are these tasks always possible within the given conditions? Are any stronger conditions needed? Are there cases with an <a href="https://mathstodon.xyz/tags/analytic" class="mention hashtag" rel="nofollow noopener" target="_blank">#analytic</a> solution, or are they possible only with numerical approximations?<a href="https://mathstodon.xyz/tags/Analysis" class="mention hashtag" rel="nofollow noopener" target="_blank">#Analysis</a> <a href="https://mathstodon.xyz/tags/DifferentialGeometry" class="mention hashtag" rel="nofollow noopener" target="_blank">#DifferentialGeometry</a> <a href="https://mathstodon.xyz/tags/Calculus" class="mention hashtag" rel="nofollow noopener" target="_blank">#Calculus</a> <a href="https://mathstodon.xyz/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#DifferentialEquations</a> <a href="https://mathstodon.xyz/tags/NumericalMethods" class="mention hashtag" rel="nofollow noopener" target="_blank">#NumericalMethods</a>

Pustam | पुस्तम | পুস্তম🇳🇵LINEAR TRANSPORT EQUATION The linear transport equation (LTE) models the variation of the concentration of a substance flowing at constant speed and direction. It's one of the simplest partial differential equations (PDEs) and one of the few that admits an analytic solution.Given \(\mathbf{c}\in\mathbb{R}^n\) and \(g:\mathbb{R}^n\to\mathbb{R}\), the following Cauchy problem models a substance flowing at constant speed in the direction \(\mathbf{c}\). \[\begin{cases} u_t+\mathbf{c}\cdot\nabla u=0,\ \mathbf{x}\in\mathbb{R}^n,\ t\in\mathbb{R}\\ u(\mathbf{x},0)=g(\mathbf{x}),\ \mathbf{x}\in\mathbb{R}^n \end{cases}\] If \(g\) is continuously differentiable, then \(\exists u:\mathbb{R}^n\times\mathbb{R}\to\mathbb{R}\) solution of the Cauchy problem, and it is given by \[u(\mathbf{x},t)=g(\mathbf{x}-\mathbf{c}t)\]<a href="https://mathstodon.xyz/tags/LinearTransportEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#LinearTransportEquation</a> <a href="https://mathstodon.xyz/tags/LinearTransport" class="mention hashtag" rel="nofollow noopener" target="_blank">#LinearTransport</a> <a href="https://mathstodon.xyz/tags/Cauchy" class="mention hashtag" rel="nofollow noopener" target="_blank">#Cauchy</a> <a href="https://mathstodon.xyz/tags/CauchyProblem" class="mention hashtag" rel="nofollow noopener" target="_blank">#CauchyProblem</a> <a href="https://mathstodon.xyz/tags/PDE" class="mention hashtag" rel="nofollow noopener" target="_blank">#PDE</a> <a href="https://mathstodon.xyz/tags/PDEs" class="mention hashtag" rel="nofollow noopener" target="_blank">#PDEs</a> <a href="https://mathstodon.xyz/tags/CauchyModel" class="mention hashtag" rel="nofollow noopener" target="_blank">#CauchyModel</a> <a href="https://mathstodon.xyz/tags/Math" class="mention hashtag" rel="nofollow noopener" target="_blank">#Math</a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="nofollow noopener" target="_blank">#Maths</a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="nofollow noopener" target="_blank">#Mathematics</a> <a href="https://mathstodon.xyz/tags/Linear" class="mention hashtag" rel="nofollow noopener" target="_blank">#Linear</a> <a href="https://mathstodon.xyz/tags/LinearPDE" class="mention hashtag" rel="nofollow noopener" target="_blank">#LinearPDE</a> <a href="https://mathstodon.xyz/tags/TransportEquation" class="mention hashtag" rel="nofollow noopener" target="_blank">#TransportEquation</a> <a href="https://mathstodon.xyz/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#DifferentialEquations</a>

Brain Dynamics ToolboxThe Modeller's Workshop for the <a href="https://mastodon.au/tags/BrainDynamicsToolbox" class="mention hashtag" rel="nofollow noopener" target="_blank">#BrainDynamicsToolbox</a> is now open for enrolments.This is an online course for researchers, students and instructors who wish to build custom dynamical models using the Brain Dynamics Toolbox. The course focuses on practical programming techniques for various classes of <a href="https://mastodon.au/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#DifferentialEquations</a> (ordinary, partial, delay, stochastic) that typically arise in <a href="https://mastodon.au/tags/ComputationalNeuroscience" class="mention hashtag" rel="nofollow noopener" target="_blank">#ComputationalNeuroscience</a>. The methods apply to other fields too. Example code is provided in all cases. Upon completing the course, students will be able to turn bespoke differential equations into working simulations. Study time is 8 hours.Course Website <a href="https://bdtoolbox.teachable.com/p/modellers-workshop" rel="nofollow noopener" translate="no" target="_blank">https://bdtoolbox.teachable.com/p/modellers-workshop</a>Toolbox Website <a href="https://bdtoolbox.org" rel="nofollow noopener" translate="no" target="_blank">https://bdtoolbox.org</a>Important Information Enrolments close 31st January 2024.

Jitse NiesenI am excited to see "Splitting methods for differential equations" by Sergio Blanes, Fernando Casas and Ander Murua on arXiv: <a href="https://arxiv.org/abs/2401.01722" rel="nofollow noopener" translate="no" target="_blank">https://arxiv.org/abs/2401.01722</a>This is a review article to be published in the excellent Acta Numerica. It discusses numerical methods for solving differential equations which can be split in several parts that are easier to solve. In formulas, the (ordinary or partial) differential equation is 𝑑𝑢/𝑑𝑡 = 𝑓(𝑢) and the splitting is 𝑓(𝑢) = 𝑓₁(𝑢) + 𝑓₂(𝑢). For people that don't do numerical analysis or computational mathematics, it may be helpful to think of the Lie–Trotter product formula \[ e^{A+B} = \lim_{n\to\infty} (e^{A/n}e^{B/n})^n. \] This is the simplest splitting method. Part of the game is to find formulas that converge faster.<a href="https://mathstodon.xyz/tags/NumericalAnalysis" class="mention hashtag" rel="nofollow noopener" target="_blank">#NumericalAnalysis</a> <a href="https://mathstodon.xyz/tags/DifferentialEquations" class="mention hashtag" rel="nofollow noopener" target="_blank">#DifferentialEquations</a> <a href="https://mathstodon.xyz/tags/SplittingMethods" class="mention hashtag" rel="nofollow noopener" target="_blank">#SplittingMethods</a>

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