@@ -9,19 +9,19 @@ to understanding the deeper parts of the documentation.
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There are three types of nonlinear systems:
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- 1 . The "standard nonlinear system", i.e. the ` NonlinearProblem ` . This is a
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- system of equations with an initial condition where you want to satisfy
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- all equations simultaniously.
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- 2 . The "interval rootfinding problem", i.e. the ` IntervalNonlinearProblem ` .
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- This is the case where you're given an interval ` [a,b] ` and need to find
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- where ` f(u) = 0 ` for ` u ` inside the bounds.
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- 3 . The "steady state problem", i.e. find the ` u ` such that ` u' = f(u) = 0 ` .
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- While related to (1), it's not entirely the same because there's a uniquely
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- defined privledged root.
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- 4 . The nonlinear least squares problem, which is an overconstrained nonlinear
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- system (i.e. more equations than states) which might not be satisfiable, i.e.
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- there may be no ` u ` such that ` f(u) = 0 ` , and thus we find the ` u ` which
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- minimizes ` ||f(u)|| ` in the least squares sense.
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+ 1 . The "standard nonlinear system", i.e. the ` NonlinearProblem ` . This is a
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+ system of equations with an initial condition where you want to satisfy
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+ all equations simultaniously.
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+ 2 . The "interval rootfinding problem", i.e. the ` IntervalNonlinearProblem ` .
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+ This is the case where you're given an interval ` [a,b] ` and need to find
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+ where ` f(u) = 0 ` for ` u ` inside the bounds.
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+ 3 . The "steady state problem", i.e. find the ` u ` such that ` u' = f(u) = 0 ` .
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+ While related to (1), it's not entirely the same because there's a uniquely
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+ defined privledged root.
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+ 4 . The nonlinear least squares problem, which is an overconstrained nonlinear
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+ system (i.e. more equations than states) which might not be satisfiable, i.e.
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+ there may be no ` u ` such that ` f(u) = 0 ` , and thus we find the ` u ` which
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+ minimizes ` ||f(u)|| ` in the least squares sense.
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For now let's focus on the first two. The other two are covered in later tutorials,
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but from the first two we can show the general flow of the NonlinearSolve.jl package.
@@ -105,7 +105,7 @@ For a complete list of solver choices, see [the nonlinear system solvers page](@
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Next we can modify the tolerances. Here let's set some really low tolerances to force a tight solution:
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``` @example 1
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- solve(prob, TrustRegion(), reltol= 1e-12, abstol= 1e-12)
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+ solve(prob, TrustRegion(), reltol = 1e-12, abstol = 1e-12)
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```
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There are many more options for doing this configuring. Specifically for handling termination conditions,
@@ -139,10 +139,10 @@ sol = solve(prob_int, ITP(), abstol = 0.01)
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Congrats, you now know how to use the basics of NonlinearSolve.jl! However, there is so much more to
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see. Next check out:
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- - [ Some code optimization tricks to know about with NonlinearSolve.jl] (@ref code_optimization)
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- - [ An iterator interface which lets you step through the solving process step by step] (@ref iterator)
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- - [ How to handle large systems of equations efficiently] (@ref large_systems)
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- - [ Ways to use NonlinearSolve.jl that is faster to startup and can statically compile] (@ref fast_startup)
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- - [ More detailed termination conditions] (@ref termination_conditions_tutorial)
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+ - [ Some code optimization tricks to know about with NonlinearSolve.jl] (@ref code_optimization)
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+ - [ An iterator interface which lets you step through the solving process step by step] (@ref iterator)
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+ - [ How to handle large systems of equations efficiently] (@ref large_systems)
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+ - [ Ways to use NonlinearSolve.jl that is faster to startup and can statically compile] (@ref fast_startup)
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+ - [ More detailed termination conditions] (@ref termination_conditions_tutorial)
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- And also check out the rest of the manual.
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+ And also check out the rest of the manual.
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