# To provide Jacobian in non-linear solver, time-stepping or Jacobian

**URL:** <https://discourse.julialang.org/t/to-provide-jacobian-in-non-linear-solver-time-stepping-or-jacobian/81632>\
**Category:** Numerics\
**Tags:** question, diffeq\
**Created:** [May 25, 2022, 6:08am UTC](https://discourse.julialang.org/t/to-provide-jacobian-in-non-linear-solver-time-stepping-or-jacobian/81632 "2022-05-25T06:08:28Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![ziolai](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ziolai/32/23422_2.png) [@ziolai](https://discourse.julialang.org/u/ziolai)\
**Post date:** [May 25, 2022, 6:08am UTC](https://discourse.julialang.org/t/to-provide-jacobian-in-non-linear-solver-time-stepping-or-jacobian/81632/1 "2022-05-25T06:08:28Z")

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Is there a good example showing that the effort of providing the Jacobian to either a non-linear solver, a time-stepping solver or an optimization solver does pay off in reducing the number of (non-linear, right-hand side or objective) function evaluations? Thx.

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**Author:** ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)\
**Post date:** [May 26, 2022, 12:40pm UTC](https://discourse.julialang.org/t/to-provide-jacobian-in-non-linear-solver-time-stepping-or-jacobian/81632/2 "2022-05-26T12:40:34Z")

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It won’t if automatic differentiation is around because that will generally be accurate enough. It’s not hard to show against finite differences though, take a very stiff equation and do something like `Rodas5(autodiff=false)` (ROBER?) and you’ll see the difference (since Rodas methods require an accurate Jacobian)

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**Author:** ![ziolai](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ziolai/32/23422_2.png) [@ziolai](https://discourse.julialang.org/u/ziolai)\
**Post date:** [May 26, 2022, 12:52pm UTC](https://discourse.julialang.org/t/to-provide-jacobian-in-non-linear-solver-time-stepping-or-jacobian/81632/3 "2022-05-26T12:52:20Z")

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Thanks. Will give its a look.