Highly Accurate Compact Finite Difference Method and its Applications : A high order numerical method for solving partial differential equations and its applications in Financial Mathematics and Compu

ISBN-13: 9783639152470 / Angielski / Miękka / 2009 / 192 str.

Jichao Zhao

Opis

This book talks about the symbolic generation offinite difference schemes, especially so-calledcompact finite difference schemes, and theirnumerical applications to elliptic equations,integro-differential equations, the American optionpricing problem, and cardiac tissue models.We take as a base Corless and Rokicki s 1995 work onautomatic generation of finite difference formulaeand numerical integration formulae of univariate andbivariate problems. We then extend this methodologyto any dimension. The new Maple routine FINDIF allowsfor automatic, symbolic discretization of variousfinite difference formulae, integration formulae, andcomputes formulae for truncation errors. Compact finite difference schemes are given forboundary value problems and elliptic partialdifferential equations. Compact finite differencemethods are also used to solve efficientlyintegro-differential equations (IDE s). Furthermore,we apply the method to solve the famous Americanoption pricing problem and simulate the actionpotential propagation through two dimensional cardiactissues. All simulation results demonstrate thecompact finite difference method is a promisingapproach.

O autorze

I obtained my Ph.D. degree in 2006 from the Department of Applied
Mathematics at University of Western Ontario, Canada. Then I
worked one year in INRIA, France as a postdoc fellow. Now I work
on atrial computer modeling in Auckland University. My research
focuses on numerical computation, and its application in Financial
Mathematics and Biology.