分数阶非线性方程近似解析解的新解法  

New approximate solutions of fractional nonlinear equations

作　　者：董立华[1] 刘艳芹[1] 

机构地区：[1]德州学院数学科学学院,山东德州253023

出　　处：《计算机工程与应用》2014年第23期1-3,25,共4页Computer Engineering and Applications

基　　金：山东省优秀中青年科学家科研奖励基金(No.BS2013HZ026);山东省自然科学基金(No.ZR2013AQ005)

摘　　要：将变分迭代法、同伦扰动法和Laplace变换相结合应用于分数阶非线性发展方程近似解的求解,其中Laplace变换可准确方便地求得分数阶的Lagrange乘子,而He的多项式可简单地处理方程中出现的非线性项,将新的处理方法应用到分数阶耦合的MKd V方程,结果表明该方法具有较高的精度和收敛性。A novel method which is based on variational iteration method, Laplace transform and homotopy perturbation method is proposed, and this new method is applied to obtain the approximate solutions of the fractional coupled MKdV equation. The fractional Lagrange multiplier is accurately determined by the Laplace transform and the nonlinear term can be easily handled by He’s polynomials. The results demonstrate accuracy and fast convergence of this new algorithm.

关 键 词：变分迭代法 LAPLACE变换 同伦扰动法 分数阶方程 非线性方程 

分 类 号：O175.29[理学—数学]