{
  "id": "2406.06008",
  "version": "v1",
  "published": "2024-06-10T04:08:17.000Z",
  "updated": "2024-06-10T04:08:17.000Z",
  "title": "Efficient algorithm for the oscillatory matrix functions",
  "authors": [
    "Dongping Li",
    "Xue Wang",
    "Xiuying Zhang"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and restoring technique based on a quadruple angle formula in conjunction with a truncated Taylor series. The choice of the scaling parameter and the degree of the Taylor polynomial relies on a forward error analysis. Numerical experiments show that the new algorithm behaves in a stable fashion and performs well in both accuracy and efficiency.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-10T04:08:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F30",
      "65F60",
      "G.1.3"
    ],
    "keywords": [
      "efficient algorithm",
      "second-order semi-linear initial value problems",
      "solving second-order semi-linear initial value",
      "general oscillatory matrix functions",
      "quadruple angle formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}