How to customize solver algorithm: May be needed in some physical problem.

[fangrh]

In the document, the code below can get a serial of solutions with time step of 1e-8.
sol = solve(prob, Tsit5(), saveat=1e-8)
However, in some case, we only concern about the sum of these solutions. To achieve this, I get a serial of solutions firstly and then calculate the sum of these solutions. This cost may memory resource since we should save all the solutions in memory.
My question is

1. Can we just calculate the sum of solutions at every step.
2. Is there possible to customize solver algorithm as like Tsit5(), TRBDF2() ...

[ChrisRackauckas]

Is there possible to customize solver algorithm as like Tsit5(), TRBDF2() ...

What do you mean?

Can we just calculate the sum of solutions at every step.

Yes, see the documentation on SavingCallback. https://diffeq.sciml.ai/stable/features/callback_library/#saving_callback

[fangrh]

Yes, see the documentation on SavingCallback. https://diffeq.sciml.ai/stable/features/callback_library/#saving_callback

Thanks very much.

What do you mean?

sol = solve(prob, alg, saveat=1e-8)
I mean how to customize algorithm for the alg argument.

[ChrisRackauckas]

Customize what?

[fangrh]

Customize OrdinaryDiffEqAlgorithm or OrdinaryDiffEqAdaptiveAlgorithm

[ChrisRackauckas]

I still have no idea what you're asking for. Customizing what about them? Do you mean https://diffeq.sciml.ai/stable/solvers/ode_solve/#Extra-Options ?

[fangrh]

I still have no idea what you're asking for. Customizing what about them? Do you mean https://diffeq.sciml.ai/stable/solvers/ode_solve/#Extra-Options ?

Although it is different from my origin diea, maybe this is a more fashionable way. Let me try. Thanks again.

[ChrisRackauckas]

Can you describe what you're asking for?

[fangrh]

I want to customized the MyCustomAlgorithm

using DifferentialEquations
f(u,p,t) = 1.01*u
u0 = 1/2
tspan = (0.0,1.0)
prob = ODEProblem(f,u0,tspan)
struct MyCustomAlgorithm <: OrdinaryDiffEqAdaptiveAlgorithm end # I want to customize a algorithm.
sol = solve(prob, MyCustomAlgorithm(), reltol=1e-8, abstol=1e-8) # And used for solve function

[ChrisRackauckas]

See the developer docs section.

https://docs.sciml.ai/dev/modules/DiffEqDevDocs/contributing/adding_packages/

https://github.com/SciML/SimpleDiffEq.jl/blob/master/src/tsit5/gpuatsit5.jl are some simple examples.