Supplementary Material and Reproducibility Archive for Variable-mass consistency for high-order transient source-corrected compact finite differences on nonuniform grids

<p dir="ltr">This dataset and supplementary material accompany the manuscript “Variable-mass consistency for high-order transient source-corrected compact finite differences on nonuniform grids.”</p><p><br></p><p dir="ltr">The study develops a variable-mass consistency principle for transient source-corrected compact finite-difference discretizations on nonuniform Cartesian grids. For the blended compact difference (BCD) method, the formulation consistently incorporates the drift-dependent mass operator into current-mass BDF2, BDF5, and BDF6 time integration, together with a three-stage fifth-order Radau-IIA startup procedure, exact Schur elimination of derivative fields, matrix-free Krylov solution, and high-order treatment of Dirichlet, Neumann, and Robin boundary conditions.

The accompanying numerical experiments examine spatial and temporal convergence, mesh-stretching robustness, mixed-boundary accuracy, stability behavior, and Schur-solver performance.</p><p><br></p><p dir="ltr">The supplementary package provides the complete BCD coefficient specification, algebraic and symbolic verification details, auxiliary numerical results, and additional verification figures. The reproducibility archive contains executable verification code, machine-readable numerical tables, reference-calculation outputs, automated tests, plotting scripts, and related files supporting reproduction and independent checking of the principal theoretical and numerical results reported in the manuscript.</p>