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1.
An effective characterization is given for a class of generalized nonlinear diffusion equations with power law dependent terms. Further, a new auxiliary equation ansatz is derived. Consequently, new exact traveling wave trigonometric function, solitary-like and Weierstrass elliptic solutions to a subclass are obtained by means of an auxiliary equation method and a generalized Riccati equation expansion method. 相似文献
2.
解非线性方程的二阶敛速指数迭代法 总被引:21,自引:0,他引:21
1.gi言文[1,2]中利用ODE方法[']给出解非线性方程在卜6I内的根x"的两个非线性迭代法其中'w由文[2]中(5)式确定.令h-1方法(2)具有M阶敛速,方法(3)是线性收敛的.它们是李雅普诺夫渐近稳定性和文[4]中Lambert提出的解Stiff方程的非线性方法相结合的结果.Lllbll't在每个小区间【Ln,Ln+1]上用一个有理函数月O一句(I十利来逼近微分方程的解z二"I,*。);*。Ek;q,使得对I_,J。)一J_,"乙十;,J。)=。_+i,l'(Ln,10)一人,而tim0(7;00)一0".那么我们能否在每个小区间【Ln,Ln+1]上用一个指… 相似文献
3.
《Journal of the Egyptian Mathematical Society》2014,22(3):390-395
In this article, new extension of the generalized and improved (G′/G)-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV) equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations. 相似文献
4.
Amit Kumar Maheshwari 《Applied mathematics and computation》2009,211(2):383-391
The present paper illustrates an iterative numerical method to solve nonlinear equations of the form f(x) = 0, especially those containing the partial and non partial involvement of transcendental terms. Comparative analysis shows that the present method is faster than Newton-Raphson method, hybrid iteration method, new hybrid iteration method and others. Cost is also found to be minimum than these methods. The beauty in our method can be seen because of the optimization in important effecting factors, i.e. lesser number of iteration steps, lesser number of functional evaluations and lesser value of absolute error in final as well as in individual step as compared to the other methods. This work also demonstrates the higher order convergence of the present method as compared to others without going to the computation of second derivative. 相似文献
5.
Li-Ying YangGuan-Ting Liu 《Applied mathematics and computation》2011,217(18):7377-7384
Using the differential transformation method and the homogeneous balance method, some new solutions of an auxiliary elliptic equation are obtained. These solutions possess the forms of rational functions in terms of trigonometric functions, hyperbolic functions, exponential functions, power functions, elliptic functions and their operation and composite functions and so on, which are so-called quasi-rational function solutions. Based on these new quasi-rational functions solutions, a direct method is proposed to construct the exact solutions of some nonlinear evolution equations with the aid of symbolic computation. The coupled KdV-mKdV equation and Broer-Kaup equations are chosen to illustrate the effectiveness and convenience of the suggested method for obtaining quasi-rational function solutions of nonlinear evolution equations. 相似文献
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7.
推广Lax-Wendroff多步方法,建立一类新的显式和隐式相结合的多步格式,并以此为基础提出了一类显隐多步-小波-Galerkin方法,可以用来求解依赖时间的偏微分方程.不同于Taylor-Galerkin方法,文中的方案在提高时间离散精度时不包含任何新的高阶导数.由于引入了隐式部分,与传统的多步方法相比该方案有更好的稳定性,适合于求解非线性偏微分方程,理论分析和数值例子都说明了方法的有效性. 相似文献
8.
夏鸿鸣 《纯粹数学与应用数学》2013,(6):577-581
研究了(2+1)维KP方程的孤子解问题.应用Riccati方程映射法,得到了(2+1)维KP方程的新的显式精确解的结构.根据得到的精确解结构,构造出了该方程的三类精确解. 相似文献
9.
施业琼 《数学的实践与认识》2009,39(16)
分析研究了一个具有三次增益效应和五次耗散项的2+1维Ginzburg-Landau方程.利用同解变型法并结合一个高阶辅助方程的解,成功地取得了该方程的一些新的精确行波解. 相似文献
10.
We introduce a new method for proving the nonexistence of positive supersolutions of elliptic inequalities in unbounded domains of ? n . The simplicity and robustness of our maximum principle-based argument provides for its applicability to many elliptic inequalities and systems, including quasilinear operators such as the p-Laplacian, and nondivergence form fully nonlinear operators such as Bellman-Isaacs operators. Our method gives new and optimal results in terms of the nonlinear functions appearing in the inequalities, and applies to inequalities holding in the whole space as well as exterior domains and cone-like domains. 相似文献