A strategy is introduced to solve canonical differential equations for Feynman master integrals on arbitrary geometries by reducing numerical evaluation to an enlarged system of rational differential equations.
CHESS: CHEbyshev pSeudo-Spectral transport for Feynman integral differential equations
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abstract
We present CHESS (CHEbyshev pSeudo Spectrum), a Wolfram Language package for high-precision one-dimensional transport of {\epsilon}-factorized differential equations for Feynman master integrals. The solver works with the matrix obtained by pulling a differential one-form to a chosen path. This matrix may be supplied directly, or assembled from constant matrices and precomputed scalar pullbacks of the one-forms. The program combines Chebyshev-Lobatto spectral collocation, sparse matrix assembly, sequential propagation in the {\epsilon}-expansion, and residue-based regularization of spurious regular singular endpoints. Benchmarks for large multi-scale integral families show rapid node convergence and agreement with independent reference data where such data are available. In the fixed local-series comparison used here, the Chebyshev transports also give shorter wall times; the reported process-tree memory usage is comparable for the smaller parallel runs and lower for the largest benchmark system in that comparison.
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Solution of Canonical Differential Equations for Integrals on Arbitrary Geometries
A strategy is introduced to solve canonical differential equations for Feynman master integrals on arbitrary geometries by reducing numerical evaluation to an enlarged system of rational differential equations.