𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The multigrid algorithm applied to a degenerate equation: A convergence analysis

✍ Scribed by Ariel Almendral Vázquez; Bjørn Fredrik Nielsen

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
735 KB
Volume
225
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we analyze the convergence properties of the Multigrid Method applied to the Black-Scholes differential equation arising in mathematical finance. We prove, for the discretized single-asset Black-Scholes equation, that the multigrid V -cycle possesses optimal convergence properties. Furthermore, through a series of numerical experiments we test the performance of the method for single-asset option problems. Throughout the paper we focus on models of European options.

📜 SIMILAR VOLUMES

A modified full multigrid algorithm for
A modified full multigrid algorithm for the Navier–Stokes equations
✍ J. Yan; F. Thiele; L. Xue 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 640 KB

A modified full multigrid (FMG) method for the solution of the Navier-Stokes equations is presented. The method proposed is based on a V-cycle omitting the restriction procedure for dependent variables but retaining it for the residuals. This modification avoids possible mismatches between the mass

Convergence of the Adomian method applie
Convergence of the Adomian method applied to a class of nonlinear integral equations
✍ I.L. El-Kalla 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 150 KB

In this work, a reliable approach for convergence of the Adomian method when applied to a class of nonlinear Volterra integral equations is discussed. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of the Adomian series solution.

A Robust Multigrid Algorithm for the Eul
A Robust Multigrid Algorithm for the Euler Equations with Local Preconditioning and Semi-coarsening
✍ D.L Darmofal; K Siu 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 321 KB

A semi-coarsened multigrid algorithm with a point block Jacobi, multi-stage smoother for second-order upwind discretizations of the two-dimensional Euler equations which produces convergence rates independent of grid size for moderate subsonic Mach numbers is presented. By modification of this base

On a quadrature algorithm for the piecew
On a quadrature algorithm for the piecewise linear wavelet collocation applied to boundary integral equations
✍ Andreas Rathsfeld; Reinhold Schneider 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 353 KB

## Abstract In this paper, we consider a piecewise linear collocation method for the solution of a pseudo‐differential equation of order r=0, −1 over a closed and smooth boundary manifold. The trial space is the space of all continuous and piecewise linear functions defined over a uniform triangula