# The Nonlinear Dame: A Case for NonlinearSolve.jl

Having just watched the GTC2024 keynote, I was wondering about how an AI would be able to explain julia packages in an engaging style, so I tried the Google Gemini Prompt:
“Write a tutorial about NonlinearSolve.jl in the style of a Raymond Chandler novel.”

## The Nonlinear Dame: A Case for NonlinearSolve.jl

The dame walked in, all curves and question marks. “It’s a problem,” she sighed, smoke curling from a cigarette like a question mark itself. “Equations gone rogue, functions flippin’ the bird to linearity. They need findin’, these roots of the equation kind.”

She wasn’t wrong. Nonlinear equations were the mean streets of mathematics, shadows twisting solutions out of sight. But me? I was Mike “The Solver” O’Malley, and I had a package in my pocket hotter than a dame in a red dress: NonlinearSolve.jl.

This package, see, was a tough guy. It didn’t play patty-cake with one-dimensional problems. It could handle functions meaner than a loan shark’s grin, with features like:

• Newton’s Law of Root Finding: This dame was a charmer, using the function’s slope to home in on the root like a heat-seeking missile. But careful, she could get temperamental with rough functions.
• Bracketing the Beast: Sometimes you gotta rough up a problem before you solve it. Bisection and Falsi methods were the muscle in this package, squeezing the equation between two points until the root sings.
• Sparse and Dangerous: This dame wasn’t afraid of a little complexity. She could handle sparse matrices, the kind that leave more empty space than a two-bit speakeasy at closing time.
• Krylov? More Like “Killer” Methods: When the going got tough, NonlinearSolve.jl brought in the big guns: Krylov methods, a whole gang of algorithms for solving large-scale problems.

Now, the dame wasn’t lookin’ for a lecture. She needed results. So, I cracked my knuckles and fired up the Julia console. The code was clean, the syntax tight. We defined the function, fed it to NonlinearSolve.jl, and let the package do its dirty work.

It wasn’t always smooth sailing. Some functions threw tantrums, some roots hid in deeper shadows than a speakeasy backroom. But NonlinearSolve.jl had options. We could swap solvers, adjust parameters, until finally, the answer popped out like a cork from a champagne bottle.

“There you go, doll,” I said, slidin’ the solution across the desk. “Roots found, equation tamed. Now, how about a drink to celebrate?”

The dame smiled, a hint of mystery still in her eyes. “Maybe another time, champ. There’s always another equation out there, waitin’ to be solved.”

And that’s the life with NonlinearSolve.jl. It’s a package for the tough cases, the dames with problems written in nonlinear code. It ain’t always easy, but when you find the root, the satisfaction is sweeter than rye whiskey on a cold night. Just remember, when the equations get mean, NonlinearSolve.jl is the muscle you need to crack the case.

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I am not exactly a fan of LLM-generated content being posted here, but I must admit—this made me laugh! Everyone wishes to be just like Mike “The Solver” O’Malley.