{
  "id": "2305.06571",
  "version": "v1",
  "published": "2023-05-11T05:14:53.000Z",
  "updated": "2023-05-11T05:14:53.000Z",
  "title": "Numerical Stability for Differential Equations with Memory",
  "authors": [
    "Guihong Wang",
    "Yuqing Li",
    "Tao Luo",
    "Zheng Ma",
    "Nung Kwan Yip",
    "Guang Lin"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some sufficient conditions for the stability and convergence of some common multi-step methods, and accordingly, a notion of A-stability for differential equations with memory. Finally, we carry out the computational performance of our theory through numerical examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-11T05:14:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "differential equations",
      "numerical stability",
      "common multi-step methods",
      "linear multi-step methods",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}