共查询到20条相似文献,搜索用时 249 毫秒
1.
2.
3.
对多层渗流方程组合系统提出适合并行计算的二阶和一阶两类迎风分数步长差分格式,利用变分形式、能量方法、二维和三维格式的配套、隐显格式的相互结合、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧,对二阶格式得到收敛性的最佳阶的L2误差估计. 对一阶格式亦得到收敛性的L2误差估计. 该方法已成功地应用到多层油资源运移聚集的评估生产实际中,得到了很好的数值模拟结果. 相似文献
4.
基于分数阶Taylor(泰勒)级数展开原理,建立单相延迟一阶分数阶近似方程,获得分数阶热传导方程.针对短脉冲激光加热问题建立分数阶热传导方程组,并运用Laplace(拉普拉斯)变换方法进行求解,给出非Gauss(高斯)时间分布的激光内热源温度场解析解.针对具体算例数值研究温度波传播特性.结果表明热传播速度与分数阶阶次有关,分数阶阶次增加,热传播速度减小,温度变化幅度增加.分数阶方程可以用于描述介于扩散方程和热波方程间的热传输过程,且对热传播机制与分数阶热传导方程中分数阶项的关系做了深入剖析. 相似文献
5.
基于分数阶微积分基本定理和三次B样条理论,构造了求解线性Caputo-Fabrizio型分数阶微分方程数值解的三次B样条方法,利用分数阶微积分基本定理将初值问题转化为关于解函数的表达式,再使用三次B样条函数逼近表达式中积分项的被积函数,进而计算了一类Caputo-Fabrizio型分数阶微分方程的数值解.给出了所构造的三次B样条方法的误差估计、收敛性和稳定性的理论证明.数值实验表明,该文数值方法在求解一类Caputo-Fabrizio型分数阶微分方程数值解时具有一定的可行性和有效性,且计算精度和计算效率优于现有的两种数值方法. 相似文献
6.
本文针对第二类端点奇异Fredholm积分方程构造基于分数阶Taylor展开的退化核方法,设计了两种计算格式,一是在全区间上使用分数阶Taylor展开式近似核函数,二是在包含奇点的小区间上采用分数阶插值,在剩余区间上采用分段二次多项式插值逼近核函数.讨论了两种退化核方法收敛的条件,并给出了混合插值法的收敛阶估计.数值算例表明对于非光滑核函数分数阶退化核方法有着良好的计算效果,且混合二次插值法比全区间上的分数阶退化核方法有着更广泛的适用范围. 相似文献
7.
8.
9.
10.
11.
12.
Hang Xu Shi-Jun Liao Xiang-Cheng You 《Communications in Nonlinear Science & Numerical Simulation》2009,14(4):1152-1156
In this paper, the time fractional partial differential equations are investigated by means of the homotopy analysis method. This technique is extended to study the partial differential equations of fractal order for the first time. The accurate series solutions are obtained. This indicates the validity and great potential of the homotopy analysis method for solving nonlinear fractional partial differential equations. 相似文献
13.
Mehdi Dehghan Jalil Manafian Abbas Saadatmandi 《Numerical Methods for Partial Differential Equations》2010,26(2):448-479
In this article, the homotopy analysis method is applied to solve nonlinear fractional partial differential equations. On the basis of the homotopy analysis method, a scheme is developed to obtain the approximate solution of the fractional KdV, K(2,2), Burgers, BBM‐Burgers, cubic Boussinesq, coupled KdV, and Boussinesq‐like B(m,n) equations with initial conditions, which are introduced by replacing some integer‐order time derivatives by fractional derivatives. The homotopy analysis method for partial differential equations of integer‐order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions of the studied models are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 相似文献
14.
Ahmet Bekir Özkan Güner Burcu Ayhan 《Mathematical Methods in the Applied Sciences》2015,38(17):3807-3817
In this paper, the ‐expansion method is proposed to establish hyperbolic and trigonometric function solutions for fractional differential‐difference equations with the modified Riemann–Liouville derivative. The fractional complex transform is proposed to convert a fractional partial differential‐difference equation into its differential‐difference equation of integer order. We obtain the hyperbolic and periodic function solutions of the nonlinear time‐fractional Toda lattice equations and relativistic Toda lattice system. The proposed method is more effective and powerful for obtaining exact solutions for nonlinear fractional differential–difference equations and systems. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
15.
Hang Xu 《Communications in Nonlinear Science & Numerical Simulation》2009,14(5):1978-1983
In this paper, we apply the homotopy analysis method (HAM) to solve the fractional Volterra’s model for population growth of a species in a closed system. This technique is extended to give solutions for nonlinear fractional integro–differential equations. The whole HAM solution procedure for nonlinear fractional differential equations is established. Further, the accurate analytical approximations are obtained for the first time, which are valid and convergent for all time t. This indicates the validity and great potential of the homotopy analysis method for solving nonlinear fractional integro–differential equations. 相似文献
16.
Fathalla A. Rihan 《Numerical Methods for Partial Differential Equations》2010,26(6):1556-1571
This article is concerned with ?‐methods for delay parabolic partial differential equations. The methodology is extended to time‐fractional‐order parabolic partial differential equations in the sense of Caputo. The fully implicit scheme preserves delay‐independent asymptotic stability and the solution continuously depends on the time‐fractional order. Several numerical examples of interest are included to demonstrate the effectiveness of the method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
17.
Bäcklund transformation of fractional Riccati equation and its applications to the space–time FDEs 下载免费PDF全文
In this paper, the Bäcklund transformation of fractional Riccati equation is presented to establish traveling wave solutions for two nonlinear space–time fractional differential equations in the sense of modified Riemann–Liouville derivatives, namely, the space–time fractional generalized reaction duffing equation and the space–time fractional diffusion reaction equation with cubic nonlinearity. The proposed method is effective and convenient for solving nonlinear evolution equations with fractional order. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
18.
Zaid M. Odibat Sunil Kumar Nabil Shawagfeh Ahmed Alsaedi Tasawar Hayat 《Mathematical Methods in the Applied Sciences》2017,40(1):40-48
This paper deals with constructing generalized ‘fractional’ power series representation for solutions of fractional order differential equations. We present a brief review of generalized Taylor's series and generalized differential transform methods. Then, we study the convergence of fractional power series. Our emphasis is to address the sufficient condition for convergence and to estimate the truncated error. Numerical simulations are performed to estimate maximum absolute truncated error when the generalized differential transform method is used to solve non‐linear differential equations of fractional order. The study highlights the power of the generalized differential transform method as a tool in obtaining fractional power series solutions for differential equations of fractional order. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
19.
时间分数阶扩散方程的数值解法 总被引:1,自引:0,他引:1
马亮亮 《数学的实践与认识》2013,43(10)
分数阶微分方程在许多应用科学上比整数阶微分方程更能准确地模拟自然现象.考虑时间分数阶扩散方程,将一阶的时间导数用分数阶导数α(0<α<1)替换,给出了一种计算有效的隐式差分格式,并证明了这个隐式差分格式是无条件稳定和无条件收敛的,最后用数值例子说明差分格式是有效的. 相似文献
20.
Mehrdad Lakestani Mehdi Dehghan Safar Irandoust-pakchin 《Communications in Nonlinear Science & Numerical Simulation》2012,17(3):1149-1162
Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. Here we construct the operational matrix of fractional derivative of order α in the Caputo sense using the linear B-spline functions. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus we can solve directly the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the new technique presented in the current paper. 相似文献