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implement adjoint ODE solver #2486

@wds15

Description

@wds15

Description

For more scalable ODE solvers in Stan, the adjoint ODE method as described in the design doc

https://github.com/stan-dev/design-docs/blob/master/designs/0027-adjoint-ode.md

should be implemented in stan-math.

Example

Please refer to the design doc for details.

Expected Output

Faster ODE results and their gradients for the case of many parameters and few ODE states.

Current Version:

v4.0.1

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