feat(bvp): add boundary value problem solver#95
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This adds the core infrastructure for solving Boundary Value Problems (BVPs). A new `BVP` trait defines the problem requirements alongside a `BvpProblem` builder pattern. The `ShootingMethod` implements a single shooting method by wrapping the BVP as an ODE, integrating over the interval using an internal ODE solver, evaluating the boundary residuals, and applying Newton-Raphson iteration with finite-difference Jacobians to locate the matching initial state. Co-authored-by: Ryan-D-Gast <148826144+Ryan-D-Gast@users.noreply.github.com>
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🎯 What
Added the core infrastructure and solver implementation for solving Boundary Value Problems (BVPs).
This includes:
BVPtrait to define the differential equation and boundary conditionsBvpProblembuilder pattern for problem configurationShootingMethodutilizing Newton-Raphson iteration to solve the BVP📊 Coverage
Unit tests were added, specifically evaluating the shooting method against a standard harmonic oscillator benchmark problem. Tests achieve target convergence reliably.
✨ Result
A fully functional Shooting Method BVP solver integrated cleanly with the existing ODE structures.
PR created automatically by Jules for task 4701906037155683725 started by @Ryan-D-Gast