Chebyshev polynomial approximations with adaptive sampling solve canonical differential equations for Feynman integrals, demonstrated to be stable and competitive for two-loop five-point cases in double precision.
IterInt: Evaluating iterated integrals via differential equations
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abstract
We introduce IterInt, a novel package implemented in both Mathematica and C++ for the numerical evaluation of iterated integrals involving arbitrary integration kernels. After the user has defined the integration kernels, IterInt transforms the iterated integrals into a system of first-order linear differential equations which can be solved efficiently and with high precision using well established libraries. IterInt is also able to automatically perform shuffle-regularisation. This makes it possible to evaluate also integrals where the integrand has a pole at the starting point of the integration path. As an illustration of our code, and also to validate it and gauge its performance, we compare the output of IterInt to the results obtained by GiNaC for ordinary and elliptic multiple polylogarithms, and also to existing results for the first few orders for banana integrals with up to four loops.
fields
hep-ph 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
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.
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Chebyshev Approximations of Feynman Integrals for Collider Physics
Chebyshev polynomial approximations with adaptive sampling solve canonical differential equations for Feynman integrals, demonstrated to be stable and competitive for two-loop five-point cases in double precision.
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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.