Solver workflow

Typical call sequence

Most DESolve runs follow the same shape:

1. Construct DESolver().
2. Set the function context, including the numerical dtype.
3. Call setup() to register methods and initialize solver state.
4. Provide the right-hand side function.
5. Set the initial solution, time interval, time step, and method.
6. Call solve().
7. Read the trajectory or final state.

Core ideas

Function signatures stay explicit

DESolve expects right-hand sides in the form:

(t, u, ctx) -> (f, jac)

That keeps numerical data flow visible:

• t is the current time
• u is the state vector
• ctx holds user-supplied context such as dtype or coefficients
• jac may be None when you do not have a Jacobian

Methods are table-driven

The solver registers built-in methods during setup(). Those method tables live in the desolve/methods_*.py modules and are selected later with set_method("...").

History is optional but useful

Use setup(keep_history=True) when you want trajectories for diagnostics, plotting, or convergence studies. If you only care about the terminal state, you can turn history off to reduce storage.

Practical advice

• Prefer set_initial_solution(...) over solve(u_ini=...) for NumPy arrays.
• Keep Jacobians consistent with the dtype stored in ctx.
• Start with simple methods like RK4 before switching to implicit or split formulations.
• When experimenting with new schemes, add the method table first and then wire it into DESolver._RegisterDefaultMethods().