Hi everyone! I would like to ask for help/suggestions/advice with my code. I am trying to solve a simple macroeconomic model (plain vanilla deterministic optimal growth) using collocation with Chebyshev polynomials. To solve collocation equations, I tried to use NLsolve.jl (trust-region and newton …

Are the equations you’re solving polynomials? If so you could try HomotopyContinuation.jl

And if it’s a low dimensional system you can try IntervalRootFinding.jl

[image] Honza9723: EulerCollResid Could you try to add the keyword inplace=false?

Hi, thank you for your response! Unfortunately, it isn’t polynomial, it is a “freestyle” nonlinear problem. I am using Chebyshev polynomials to approximate the unknown function (C) in the (economics) Euler equation by forcing this approximate Euler equation to hold exactly at some pre-specified gri…

Thank you for the suggestion! Unfortunately, it didn’t work. I want to ask, is my function EulerCollocation, EulerCollResid correctly specified for NLsolve.jl? I worry, that I made some mistake there…

So I have used Chebyshev projection to solve these kinds of models but what I found was that doing it strictly by colocation was generally not very stable. As you say, unless the initial guess is very good, it can/will fail. There were two hybrid methods that I started to use. You can use Cheb. colo…

You are right, but this quess should be good enought, people are ushually solving this model using coefficients from linear approximation as initial guess (much worse than mine). I am literally starting at correct approximation, and when I try epsilon-deviation from this known solution, NLsove diver…

Great. Also, I noticed that you have a bunch of let in your function definitions. Those are not necessary and could conceivably confuse things. Potentially harmless, and definetely not helpful to always use that pattern. Functions introduce their own scope already.

NLsolve.jl collocation divergence

Specific Domains Finance and Economics

Honza9723 March 3, 2020, 7:50pm 9

Thank you all, I managed to solve the problem using this reference. Parametrize NLsolve function

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NLsolve.jl collocation divergence

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