一类四阶微积分方程的四阶差分格式  

FOURTH-ORDER DIFFERENCE METHOD FOR A CLASS OF FOURTH-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

作　　者：蔡耀雄 任全伟[1] 庄清渠[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《数值计算与计算机应用》2014年第1期59-68,共10页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金资助项目(No.11126330);福建省自然科学基金资助项目(No.2011J05005)

摘　　要：针对由吊桥模型而建立的四阶微积分方程,提出了四阶差分格式进行求解.对线性项采用紧格式进行离散,积分项则采用复化辛普森求积公式处理,再结合Newton型迭代法对方程进行求解.给出了差分格式解的存在性和收敛性的证明.数值结果表明格式的精度为O(h^4).A fourth-order finite difference method is proposed to solve the fourth-order integro- differential equation arising from the span suspension bridge model. The linear term and integral term are deal with compact difference scheme and Composite Simpson＇s Rule re- spectively. Then the equation is solved via Newton type iteration methods. The existence and convergence of the method are also proved. Numerical results show that the accuracy of the method is of O（h4）.

关 键 词：四阶微积分方程 紧差分格式 复化辛普森求积公式 迭代算法 

分 类 号：O241.8[理学—计算数学]