Cauchy initial value problem solver
A research repo exploring how adaptive linear approximation behaves near thin stiff layers. It proposes a threshold law for when layers control node placement, introduces a diagnostic fingerprint for subcritical inversion, and backs both with derivations, simulations, plots, and practical Python examples.
Yet Another BDF Integrator: variable-order BDF1–6 for stiff ODEs with forward, adjoint and simultaneous sensitivities. C++17; external CppAD, BLAS and LAPACK.
Numerical resolution and stability analysis of a system of ordinary differential equations (ODEs) with high stiffness coefficient, using homogeneous, non-homogeneous and adaptive meshes. Implements Radau_IIA, Gauss-Legendre, BDF, Crank-Nicolson, Implicit Euler and Pareschi-Russo with LU factorization optimization.
Divide-and-conquer Sobolev gradient solver for stiff ODEs — the original 2005 C++ preserved, plus a modern C++20 port that reproduces the published results
MATLAB benchmark suite for comparing numerical integrators on classical differential-equation problems, including linear decay, harmonic oscillator, Van der Pol, Lorenz, Robertson kinetics, and Kepler two-body dynamics. The repository includes performance plots, accuracy metrics, conservation analysis, and a simulation video available on YouTube.
The numerical method of lines for engineering PDEs: a validated NumPy toolkit (stencils, ghost-point boundaries, flux limiters, spectral derivatives, stiffness analysis, banded-Newton implicit integrators), 36 worked examples with exact solutions, and a 16-notebook course with solutions.
KineticsLab: implicit solver for the stiff 6-group reactor point-kinetics equations, validated to 6.6e-10 vs a scipy oracle and closed-form inhour solutions, plus protection trip logic with 0 false/0 missed trips on 120 labeled transients.
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