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In this paper, we propose an iterative approach to increase the computation efficiency of the homotopy analysis method (HAM), a analytic technique for highly nonlinear problems. By means of the Schmidt–Gram process (Arfken et al., 1985)  [15], we approximate the right-hand side terms of high-order linear sub-equations by a finite set of orthonormal bases. Based on this truncation technique, we introduce the MMth-order iterative HAM by using each MMth-order approximation as a new initial guess. It is found that the iterative HAM is much more efficient than the standard HAM without truncation, as illustrated by three nonlinear differential equations defined in an infinite domain as examples. This work might greatly improve the computational efficiency of the HAM and also the Mathematica package BVPh for nonlinear BVPs.  相似文献
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In this paper, a novel iterative method is proposed to obtain approximate-analytical solutions for the linear systems of first-order fuzzy differential equations (FDEs) with fuzzy constant coefficients (FCCs) while avoiding the complexities of eigen-value computations. A theorem for the convergence and the validity of the approach is also presented in detail. Numerical experiments and comparisons with exact solutions reveal that the proposed method is capable of generating accurate results.  相似文献
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利用自治力学系统的哈密顿函数为守恒量的性质,提出一种求非线性二阶微分方程多模态近似解析解的方法,称为哈密顿函数法.首先,介绍哈密顿函数法求多模态近似解的基本理论.其次,以质点在旋转的抛物线上运动为模型建立强非线性二阶微分方程.最后,用哈密顿函数法求得在给定初始条件和参数下强非线性二阶微分方程的三模态近似解析解表达式,作出三模态近似解析解的解曲线,并与直接用Mathematica软件作出的解曲线进行比较,讨论三模态近似解析解的精确性.结果表明:用哈密顿函数法求得的三模态近似解析解的解曲线与直接用Mathematica软件作出的解曲线十分吻合.  相似文献
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