𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Fourth-order compact schemes with adaptive time step for monodomain reaction–diffusion equations

✍ Scribed by E.A. Heidenreich; J.F. Rodríguez; F.J. Gaspar; M. Doblaré

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
1003 KB
Volume
216
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

Multigrid applied to fourth-order compact schemes for monodomain reaction-diffusion equations in two dimensions has been developed. The scheme accounts for the anisotropy of the medium, allows for any cellular activation model to be used, and incorporates an adaptive time step algorithm. Numerical simulations show up to a 40% reduction in computational time for complex cellular models as compared to second-order schemes for the same solution error. These results point to high-order schemes as valid alternatives for the efficient solution of the cardiac electrophysiology problem when complex cellular activation models are used.

📜 SIMILAR VOLUMES

An explicit fourth-order compact finite
An explicit fourth-order compact finite difference scheme for three-dimensional convection-diffusion equation
✍ Zhang, Jun 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 141 KB 👁 2 views

We present an explicit fourth-order compact ®nite dierence scheme for approximating the threedimensional convection±diusion equation with variable coecients. This 19-point formula is de®ned on a uniform cubic grid. We compare the advantages and implementation costs of the new scheme with the standar

Fourth-order compact scheme with local m
Fourth-order compact scheme with local mesh refinement for option pricing in jump-diffusion model
✍ Spike T. Lee; Hai-Wei Sun 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 161 KB

## Abstract The value of a contingent claim under a jump‐diffusion process satisfies a partial integro‐differential equation. A fourth‐order compact finite difference scheme is applied to discretize the spatial variable of this equation. It is discretized in time by an implicit‐explicit method. Mea

Multigrid Method and Fourth-Order Compac
Multigrid Method and Fourth-Order Compact Scheme for 2D Poisson Equation with Unequal Mesh-Size Discretization
✍ Jun Zhang 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 93 KB

A fourth-order compact difference scheme with unequal mesh sizes in different coordinate directions is employed to discretize a two-dimensional Poisson equation in a rectangular domain. Multigrid methods using a partial semicoarsening strategy and line Gauss-Seidel relaxation are designed to solve t