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Executable Science local pilot drafts
Use rational arithmetic to compare composite quadrature errors for x^4 on [0,1] across five nested grid resolutions.
Investigate What convergence pattern appears without floating-point rounding for these two quadrature rules?
Executable Science local pilot drafts
Sweep sixteen step sizes for forward and central differentiation of exp(x) at zero, exposing truncation and rounding behavior against the analytical derivative.
Investigate How does derivative error change across a fixed grid of shrinking step sizes?
Upstream project repository
Finite-volume partial differential equation solving for transport and related numerical models.
Investigate How do grid and time-step refinement affect error in a one-dimensional diffusion problem?
Upstream project repository
Python interfaces for HEALPix spherical pixelization and map analysis.
Investigate Do pixel centers and equal-area weights recover the integral of a constant spherical map?
SciPy documentation
An official guide to quadrature from functions or samples, multiple integration and initial-value ODE solving.
Investigate How do selected quadrature rules behave on smooth, oscillatory and endpoint-singular functions with independently known integrals?
SciPy documentation
An interpolation guide organized by data geometry, smoothness and shape requirements, including structured and scattered data.
Investigate When monotone samples are supplied, which interpolants preserve monotonicity and what approximation error do they incur?
Upstream project repository
Grid and process-model components for Earth-surface dynamics simulations.
Investigate Does a fixed landscape-diffusion component reproduce an analytic mode and the declared boundary behavior?
Upstream project repository
Audio and music-signal analysis tools, including transforms and feature extraction.
Investigate How do window size and centering affect the measured spectral peak of a synthetic sinusoid?
SciPy documentation
A guide to dense linear systems, least squares, matrix factorizations, eigenproblems and matrix functions.
Investigate How do residuals and solution errors differ as a known linear system becomes ill-conditioned?
Upstream project repository
Processing and analysis tools for electrophysiological recordings such as EEG and MEG.
Investigate How does a specified filter alter known-frequency components and edge samples in a generated signal?
Upstream project repository
Arbitrary-precision real and complex arithmetic with special functions and numerical calculus.
Investigate How does precision growth change the residual in a cancellation-sensitive special-function identity?
Upstream project repository
Graph construction, traversal, structural analysis, and network algorithms in Python.
Investigate Do weighted shortest-path routines match exhaustive simple-path enumeration on bounded positive-weight graphs?
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