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We prove the $L^2$ convergence of order $\\mathcal{O}(\\tau^{1/2})$ for this scheme with initial data in the space $H^1 (\\mathbb{R}^d)$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1610.06028","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-19T14:22:56Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"b6c7c16eebac77be0f1c2a2bca239c2598270dcf0e0dcdaba8180c7a317f3389","abstract_canon_sha256":"d74dd0e986be35e9ac7ff2f4c07c22af450025635d017da1bebd64e29006dd7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:02.475271Z","signature_b64":"xV6acmg/AvVqEe3BvzilSrMFV1lGfn0ksJe3hvar8QtiKPq4vjwyujmQqGDw5aa5vpAC3Vxjrz4Fy7yY8pd1AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ebf3bca665e1c9c90ee4a0529fff931c6e76d6f5143d9393f5f31f39ccb4622","last_reissued_at":"2026-05-17T23:48:02.474736Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:02.474736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the splitting method for the nonlinear Schr\\\"odinger equation with initial data in $H^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Woocheol Choi, Youngwoo Koh","submitted_at":"2016-10-19T14:22:56Z","abstract_excerpt":"In this paper, we establish a convergence result for the operator splitting scheme $Z_{\\tau}$ introduced by Ignat, with initial data in $H^1$, for the nonlinear Schr\\\"odinger equation :\n  $$\n  \\partial_t u = i \\Delta u + i\\lambda |u|^{p} u,\\qquad u (x,0) =\\phi (x),\n  $$ where $(x,t) \\in \\mathbb{R}^d \\times [0,\\infty)$, with $0< p < 4/(d-2)$ for $d\\geq3$ and $0< p<\\infty$ for $d=1,2$. 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