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Update docs/src/tutorials/advanced.md
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Co-authored-by: Christopher Rackauckas <accounts@chrisrackauckas.com>
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ErikQQY and ChrisRackauckas authored Sep 16, 2023
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# Solving Large Ill-Conditioned Nonlinear Systems with NonlinearSolve.jl

This tutorial is for getting into the extra features of using NonlinearSolve.jl. Solving stiff ordinary differential equations requires specializing the linear solver on properties of the Jacobian in order to cut down on the ``\mathcal{O}(n^3)`` linear solve and the ``\mathcal{O}(n^2)`` back-solves. This tutorial is designed to explain the advanced usage of NonlinearSolve.jl by solving stiff Brusselator partial differential equation (BRUSS) using NonlinearSolve.jl.
This tutorial is for getting into the extra features of using NonlinearSolve.jl. Solving ill-conditioned nonlinear systems requires specializing the linear solver on properties of the Jacobian in order to cut down on the ``\mathcal{O}(n^3)`` linear solve and the ``\mathcal{O}(n^2)`` back-solves. This tutorial is designed to explain the advanced usage of NonlinearSolve.jl by solving the steady state stiff Brusselator partial differential equation (BRUSS) using NonlinearSolve.jl.

## Definition of the Brusselator Equation

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