{
  "id": "2001.03974",
  "version": "v1",
  "published": "2020-01-12T18:34:04.000Z",
  "updated": "2020-01-12T18:34:04.000Z",
  "title": "High order semi-implicit multistep methods for time dependent partial differential equations",
  "authors": [
    "Giacomo Albi",
    "Lorenzo Pareschi"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We consider the construction of semi-implicit linear multistep methods which can be applied to time dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As shown in Boscarino, Filbet and Russo (2016) for Runge-Kutta methods, these semi-implicit techniques give a great flexibility, and allows, in many cases, the construction of simple linearly implicit schemes with no need of iterative solvers. In this work we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype linear advection-diffusion equation and in the setting of strong stability preserving (SSP) methods. Our findings are demonstrated on several examples, including nonlinear reaction-diffusion and convection-diffusion problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-12T18:34:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65L06",
      "65M12",
      "35K57",
      "76Rxx"
    ],
    "keywords": [
      "time dependent partial differential equations",
      "high order semi-implicit multistep methods",
      "semi-implicit linear multistep"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}