# Normalize the solution during the integration by differentialequations.jl

**URL:** <https://discourse.julialang.org/t/normalize-the-solution-during-the-integration-by-differentialequations-jl/70845>\
**Category:** Machine Learning\
**Tags:** diffeq\
**Created:** [November 3, 2021, 5:36am UTC](https://discourse.julialang.org/t/normalize-the-solution-during-the-integration-by-differentialequations-jl/70845 "2021-11-03T05:36:09Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![TravellingLight6](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/travellinglight6/32/30408_2.png) [@TravellingLight6](https://discourse.julialang.org/u/TravellingLight6)\
**Post date:** [November 3, 2021, 5:36am UTC](https://discourse.julialang.org/t/normalize-the-solution-during-the-integration-by-differentialequations-jl/70845/1 "2021-11-03T05:36:09Z")

</div>

I usually come to solve outwards ode like schrodinger equation under columb potential and I recently realize that the initial condition and time span affect the stability of the solution as posted as following:

```julia
using DifferentialEquations,Plots,Roots;
pyplot()

function columbode!(du,u,p,r)
    v(r)=-1/r
    du[1]=u[2]
    du[2]=(v(r)-p)*u[1]
end

f(x)=let u0=[0.0,x],rspan=(1e-10,80.0)
    prob(e)=ODEProblem(columbode!,u0,rspan,e)
    solf(e)=solve(prob(e), Tsit5(), reltol=1e-8, abstol=1e-8)
    e_eigen=find_zero(e->solf(e).u[end][1],(-1.0,-0.1))
    plot(solf(e_eigen),vars=[1])
end
display(plot(f(1e-3),f(3e-3),f(6e-3),f(1e-2),layout=(2,2)))
savefig("discourse_rescaling_ode.png")

```

![discourse_rescaling_ode](https://global.discourse-cdn.com/julialang/original/3X/2/a/2a990429c770e42a05c4105305a864aeed0ddd0c.png)

I tested four different initial derivative and found the final solutions perform differently. Only one of them behaves normally. I wonder if there’s way to deal with stability of outwards ode. Currently, I wonder if I can normalize the intermediate sol during integration using callback or integrator interface and I have no good ideas since these operations may corrupt the interpolations stuff. Thanks for any help!

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<div class="post-metadata">

**Author:** ![TravellingLight6](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/travellinglight6/32/30408_2.png) [@TravellingLight6](https://discourse.julialang.org/u/TravellingLight6)\
**Post date:** [November 3, 2021, 5:38am UTC](https://discourse.julialang.org/t/normalize-the-solution-during-the-integration-by-differentialequations-jl/70845/2 "2021-11-03T05:38:25Z")

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A specific question I want to ask is: is it possible to modify the entire sol.u like normalize it using callback or integrator interface?