{"paper":{"title":"An L-Stable Implicit Two-Stage Fourth-Order Temporal Discretization Scheme for Lax-Wendroff-Type Solvers Applied to Stiff Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"An implicit two-stage fourth-order scheme brings L-stability to Lax-Wendroff solvers for stiff problems.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Zhixin Huo","submitted_at":"2025-12-01T12:50:25Z","abstract_excerpt":"The explicit two-stage fourth-order (TSFO) temporal-spatial coupling method is efficient and compact but suffers severe time-step restrictions for stiff problems with multiple scales. To address Professor Jiequan Li's call for an implicit extension, this paper first constructs an implicit TSFO time discretization scheme using the method of undetermined coefficients and Taylor expansion. Second, using a model equation and the maximum modulus principle, sufficient conditions for L-stability are derived. Third, a Newton iteration accelerates convergence. Numerical experiments on classical stiff b"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Numerical experiments on classical stiff benchmarks show that the proposed implicit scheme achieves fourth-order temporal accuracy in two stages. Compared to the classical fourth-order implicit Runge-Kutta method, it allows larger stable time steps and reduces convergence errors by an order of magnitude.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The L-stability conditions derived from a linear model equation via the maximum modulus principle extend to the nonlinear systems and coupled spatial discretizations in Lax-Wendroff-type solvers for stiff problems.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An L-stable implicit two-stage fourth-order temporal discretization scheme is constructed for Lax-Wendroff-type solvers on stiff problems, achieving fourth-order accuracy with larger time steps than classical implicit Runge-Kutta methods.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"An implicit two-stage fourth-order scheme brings L-stability to Lax-Wendroff solvers for stiff problems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6ba1330148befb03cf137c1ed598e4d77cf809f5d1e8e34333910260aedfedbf"},"source":{"id":"2512.01628","kind":"arxiv","version":4},"verdict":{"id":"40712356-989e-4dd8-9233-afffaa0339f2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T03:10:24.754184Z","strongest_claim":"Numerical experiments on classical stiff benchmarks show that the proposed implicit scheme achieves fourth-order temporal accuracy in two stages. Compared to the classical fourth-order implicit Runge-Kutta method, it allows larger stable time steps and reduces convergence errors by an order of magnitude.","one_line_summary":"An L-stable implicit two-stage fourth-order temporal discretization scheme is constructed for Lax-Wendroff-type solvers on stiff problems, achieving fourth-order accuracy with larger time steps than classical implicit Runge-Kutta methods.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The L-stability conditions derived from a linear model equation via the maximum modulus principle extend to the nonlinear systems and coupled spatial discretizations in Lax-Wendroff-type solvers for stiff problems.","pith_extraction_headline":"An implicit two-stage fourth-order scheme brings L-stability to Lax-Wendroff solvers for stiff problems."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.01628/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"4398cafcf89bbdf044042fea419051238c4a2e3769e386b9e53e8b451771fc4c"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}