解高阶抛物型方程的三层显式差分格式  

A Three-Layer Explicit Difference Scheme for Solving the Parabolic Equation of Higher Order

作　　者：单双荣[1] 

机构地区：[1]华侨大学数学系,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2005年第3期239-242,共4页Journal of Huaqiao University(Natural Science)

基　　金：国务院侨务办公室科研基金资助项目(04QZR09)

摘　　要：对高阶抛物型方程提出一个三层显式差分格式,其局部截断误差阶是O(τ2+h4).证明当m为1,2,3时,其稳定性条件为r=τ/h2m<1/22m-1.数值例子表明所提的格式是有效的,理论分析是正确的.A three-layer explicit difference scheme is proposed for solving the parabolic equation of higher order [SX(] u[] t[SX)]=(-1) m+1 [SX(] 2m u[] t 2m [SX)] (where m is a positive integer). The local truncation error of the propesed scheme is in the order of O(τ 2+h 4) . Its stability condition is proved to be r=τ/h 2m <1/2 2m-1 when m =1,2,3. The proposed scheme is effective and relevant theoretical analysis is correct, as shown by numerical examples.

关 键 词：高阶抛物型方程 高精度 显式差分格式 

分 类 号：O241.82[理学—计算数学]