分数阶Fornberg-Whitham方程及其改进方程的变分迭代解  

Variational Iteration Solutions for Fractional Fornberg-Whitham Equation and Its Modified Equation

作　　者：鲍四元[1] 邓子辰[2,3] 

机构地区：[1]苏州科技学院土木工程学院工程力学系,江苏苏州215011 [2]西北工业大学工程力学系,西安710072 [3]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116023

出　　处：《应用数学和力学》2013年第12期1236-1246,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(11202146)~~

摘　　要：给出分数阶Fornberg-Whitham方程(FFW)并把其中非线性项uu x换为u2u x后所得的改进Fornberg-Whitham方程的解.使用了分数阶变分迭代法(fractional variational iteration method,FVIM),其中Lagrange乘子由泛函和Laplace变换确定.讨论了分数阶次的数值在两种情况下FFW方程的解,因为确定FFW方程中时间微分的阶次需要比较原方程中含时间的两个微分的阶次.最后,给出两个使用分数阶变分迭代法的算例.算例结果证明了所提方法的有效性.The solutions to the fractional Fornberg-Whitham （FFW） equation and the modified FFW equation generated by change of one nonlinear term uu with u2ux were presented. The frac- tional variational iteration method （FVIM） was used, in which the Lagrange multiplier was de- termined with the variational function and the Laplace transformation. Two cases were dis- cussed respectively for the FFW equation because the order of time differentiation was deter- mined through comparison of the two derivatives＇ orders in the fractional differential equation. Finally, two numerical examples of the FVIM solution were given. The computational results demonstrate the high efficiency of the presented method.

关 键 词：分数阶Fornberg—Whitham方程 分数阶变分迭代法 LAGRANGE乘子 近似解 初值问题 

分 类 号：O175.29[理学—数学]