共查询到17条相似文献,搜索用时 93 毫秒
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对(G′/G)展开法做了进一步的研究,利用两次函数变换将二阶非线性辅助方程的求解问题转化为一元二次代数方程与Riccati方程的求解问题.借助Riccati方程的B?cklund变换及解的非线性叠加公式获得了辅助方程的无穷序列解.这样,利用(G′/G)展开法可以获得非线性发展方程的无穷序列解,这一方法是对已有方法的扩展,与已有方法相比可获得更丰富的无穷序列解.以(2+1)维改进的Zakharov-Kuznetsov方程为例得到了它的无穷序列新精确解.这一方法可以用来构造其他非线性发展方程的无穷序列解. 相似文献
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应用同伦分析法研究微重力环境下圆管毛细流动解析近似解问题, 给出了级数解的表达公式. 不同于其他解析近似方法, 该方法从根本上克服了摄动理论对小参数的过分依赖, 其有效性与所研究的非线性问题是否含有小参数无关, 适用范围广. 同伦分析法提供了选取基函数的自由, 可以选取较好的基函数, 更有效地逼近问题的解, 通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度, 同伦分析法为圆管毛细流动问题的解析近似求解开辟了一个全新的途径. 通过具体算例, 将同伦分析法与四阶龙格库塔方法数值解做了比较, 结果表明, 该方法具有很高的计算精度.
关键词:
圆管
微重力
毛细流动
同伦分析法 相似文献
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应用同伦分析法研究无限长柱体内角毛细流动解析近似解问题,给出了级数解的递推公式.不同于其他解析近似方法,该方法从根本上克服了摄动理论对小参数的过分依赖,其有效性与所研究的非线性问题是否含有小参数无关,适用范围广.同伦分析法提供了选取基函数的自由,可以选取较好的基函数,更有效地逼近问题的解,通过引入辅助参数和辅助函数来调节和控制级数解的收敛区域和收敛速度,同伦分析法为内角毛细流动问题的解析近似求解开辟了一个全新的途径.通过具体算例,将同伦分析法与四阶龙格库塔方法数值解做了比较,结果表明,该方法具有很高的计算精度. 相似文献
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研究了一类非线性燃烧模型.利用同伦分析方法,得到了该模型的近似解.
关键词:
非线性方程
燃烧模型
同伦分析法
近似解 相似文献
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Solutions of Heat-Like and Wave-Like Equations with Variable Coefficients by Means of the Homotopy Analysis Method 下载免费PDF全文
A. K. Alomari M. S. M. Noorani R. Nazar 《中国物理快报》2008,25(2):589-592
We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter h, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method. 相似文献
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The main purpose of this paper is to find the exact and approximate analytical solution of Nizhnik–Novikov–Veselov system which may be considered as a model for an incompressible fluid with newly defined conformable derivative by using \(G'/G\) expansion method and homotopy analysis method (HAM) respectively. Authors used conformable derivative because of its applicability and lucidity. It is known that, the NNV system of equations is an isotropic Lax integrable extension of the well-known KdV equation and has physical significance. Also, NNV system of equations can be derived from the inner parameter-dependent symmetry constraint of the KP equation. Then the exact solutions obtained by using \(G'/G\) expansion method are compared with the approximate analytical solutions attained by employing HAM. 相似文献
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Zaid M. Odibat 《Physics letters. A》2008,372(8):1219-1227
This Letter deals with compact and noncompact solutions for nonlinear evolution equations with time-fractional derivatives. We present a reliable approach of the homotopy perturbation method to handle nonlinear fractional evolution equations. The validity of the approach is verified through illustrative examples. New exact solitary wave and compacton solutions are developed. The proposed technique could lead to a promising approach for a wide class of nonlinear fractional evolution equations. 相似文献
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Saeed Dinarvand 《Central European Journal of Physics》2009,7(1):114-122
The similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid
over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic
field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically
solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system
of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions
is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter
and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution
for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int.
J. Nonlinear Mech. 41, 527 (2006)].
相似文献
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Backlünd transformation and multiple soliton solutions for the (3+1)-dimensional Nizhnik-Novikov-Veselov equation 下载免费PDF全文
We develop an approach to construct multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional Nizhnik-Novikov-Veselov (NNV) equation as an example. Using the extended homogeneous balance method, one can find a Backlünd transformation to decompose the (3+1)-dimensional NNV into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional NNV equation are obtained by introducing a class of formal solutions. 相似文献
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Nonlinear Evolution Equations with Gradient Coupled Noise 总被引:1,自引:0,他引:1
We show existence and uniqueness of solutions for a class of nonlinear evolution equations with gradient coupled noise. Our results are obtained by using a simple transformation relating the equation under consideration to an underlying deterministic partial differential equation. Both the Itô and the Stratonovich conventions are treated. Several examples show that the properties of solutions for Itô equations can differ significantly from those of Stratonovich equations. 相似文献