BundleSolver setup too restrictive

[shuheng-liu]

The following code block assumes each bundle parameter must fall into one of the following categories.

1. a parameter that only appears in the boundary/initial condition (NOT in the equation); or
2. a parameter that only appears in the equation (NOT in the boundary/initial condition) https://github.com/NeuroDiffGym/neurodiffeq/blob/a3df9fd221223a85ebc973002b8e3d2b280cbc19/neurodiffeq/solvers.py#L1318-L1332

However, in theory, there should be a case where the parameter appears both in the equation and in the initial/boundary condition. The var here probably implies a parameter that appears only in the equation. A fix is needed.

[shuheng-liu]

Plus, here's my interpretation of line 1331. It might be helpful to anyone else trying to understand what the non_var_filter is doing.

• len(conditions) is the number of functions to solve for
• + 1 is hard-coded number of free variables/coordinates/inputs to functions. Since this is an ODE solver, there's only 1 input.
• + n is the index of a var (a parameter that appears only in the condition). It's deleted since the var doesn't appear in the equation by assumption.
• - i accounts for the fact that at step i (starting from 0), a total of i vars have been previously deleted. This assumes previously deleted vars appear before the current var (i.e., non_var list is sorted)! Which is not guaranteed by line 1326 and can lead to unnoticeable bugs!