{"paper":{"title":"Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic Differentiation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Andreas Griewank, Manuel Radons, Richard Hasenfelder, Tom Streubel","submitted_at":"2017-01-03T16:50:10Z","abstract_excerpt":"In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \\(F:\\R^n\\to\\R^n\\). When applied to such a problem the classical trapezoidal rule suffers from a loss of accuracy if the solution trajectory intersects a nondifferentiability of \\(F\\). The advantage of the proposed generalized trapezoidal rule is threefold: Firstly we can achieve a higher convergence order than with the classical method. Moreover, the method is energy preserving for piecewise linear Hamiltonian systems. Finally, in analogy to the classical case we derive a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00745","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}