非线性Leland方程的一种并行本性差分方法  

A KIND OF DIFFERENCE METHOD WITH INTRINSIC PARALLELISM FOR NONLINEAR LELAND EQUATION

作　　者：吴立飞[1] 杨晓忠[1] 张帆[1] 

机构地区：[1]华北电力大学数理学院,北京102206

出　　处：《数值计算与计算机应用》2014年第1期69-80,共12页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11371135;10771065);中央高校基本科研业务费专项资金资助(13QN30);北京市共建项目专项资助(2012年)

摘　　要：非线性Leland方程(支付交易费用的期权定价模型)数值解法的研究具有重要的实际意义,本文对非线性Leland方程构造了一种具有并行本性的差分格式一一交替分段Crank-Nicolson(ASC-N)格式,给出差分格式解的存在唯一性、稳定性分析及解的误差估计,理论分析表明ASCN格式为无条件稳定的并行差分格式.数值试验显示ASC-N格式的计算精度与经典的CrankNicolson格式相当,但其计算时间要比经典的Crank-Nicolson格式节省将近50%,数值试验验证了理论分析,表明本文的ASC-N格式对求解非线性Leland方程是有效的.It is very important to study the numerical solution of nonlinear Leland equation （option pricing model with transaction costs）. For solving nonlinear Leland equation, a difference method with intrinsic parallelism-Alternating Segment Crank-Nicolson （ASC-N） scheme is constructed in this paper. Then the existence and uniqueness, computational stability and error estimate of ASC-N scheme are analyzed. Theoretical analysis demonstrates that ASC-N scheme is unconditional stability parallel difference scheme. Numerical experiment demon- strates that computational accuracy of ASC-N scheme is closed to classics Crank-Nicolson scheme. But the computational time of ASC-N scheme can save nearly 50% for classic- s Crank-Nicolson scheme. Theoretical analysis and numerical experiment demonstrate the superiority of ASC-N scheme for solving nonlinear Leland equation.

关 键 词：非线性Leland方程 交替分段Crank—Nicolson(ASC—N)格式 并行计算 稳定性 数值试验 

分 类 号：O241.82[理学—计算数学]