解微分方程组的Adams预测校正算法的改进方法  

Improvement on Adams Predictor-Corrector Method Solving Systems of Differential Equations

作　　者：廖大乾[1] 杜廷松[1] 蹇继贵[1] 

机构地区：[1]三峡大学理学院数学系,湖北宜昌443002

出　　处：《大学数学》2013年第4期39-43,共5页College Mathematics

基　　金：国家自然科学基金资助项目(61174216;61074091)

摘　　要：针对Adams预测校正算法求解微分方程组作了改进.算法的主要改进之处是在校正环节用已经计算出来的"新值"取代"旧值".最后,基于提出的改进方法和传统的Adams预测校正算法对同一微分方程组问题作了数值比较实验.数值实验结果表明改进的算法与传统的Adams预测校正算法的计算量一样,但精度大大提高.The Adams predictor-corrector method is improved to solve systems of differential equations. The major improvement of the proposed new algorithm is that it adopts the new value to replace the old value at the each corrector iteration step. In the last, the proposed improvement algorithm and the traditional Adams predictor-corrector method have been implemented for same systems of differential equations problem. Some computational results are included. Computation results indicate that the computational effort of improved method is equal to the traditional Adams predictor- corrector method, but the accuracy of the improved method is higher.

关 键 词：Adams预测校正算法 微分方程组 线性多步长方法 

分 类 号：O241[理学—计算数学]