4. Solution Strategy

The following architectural decisions have been made for bice:

• Problem-Equation-Solver Decomposition: Separating the mathematical problem definition (Problem) from its governing equations (Equation) and the numerical algorithms (ContinuationStepper, NewtonSolver).

• Flexible Discretization: Providing base classes (Equation, FiniteDifferencesEquation) to allow users to implement different numerical schemes.

• Pseudo-Arclength Continuation: Defaulting to pseudo-arclength continuation for its robustness near folds and turning points.