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1.
    
In this paper, we apply the boundary integral equation technique and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of linear and nonlinear time‐fractional partial differential equations (TFPDEs). The main aim of the present paper is to examine the applicability and efficiency of DRBEM for solving TFPDEs. We employ the time‐stepping scheme to approximate the time derivative, and the method of linear radial basis functions is also used in the DRBEM technique. This method is improved by using a predictor–corrector scheme to overcome the nonlinearity that appears in the nonlinear problems under consideration. To confirm the accuracy of the new approach, several examples are presented. The convergence of the DRBEM is studied numerically by comparing the exact solutions of the problems under investigation. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

2.
    
In this paper, a fast second‐order accurate difference scheme is proposed for solving the space–time fractional equation. The temporal Caputo derivative is approximated by ?L2 ‐1σ formula which employs the sum‐of‐exponential approximation to the kernel function appeared in Caputo derivative. The second‐order linear spline approximation is applied to the spatial Riemann–Liouville derivative. At each time step, a fast algorithm, the preconditioned conjugate gradient normal residual method with a circulant preconditioner (PCGNR), is used to solve the resulting system that reduces the storage and computational cost significantly. The unique solvability and unconditional convergence of the difference scheme are shown by the discrete energy method. Numerical examples are given to verify numerical accuracy and efficiency of the difference schemes.  相似文献   

3.
Arnold  C. 《Numerical Algorithms》1997,15(1):111-134
Introducing the notion of the formal continued fractions solutions of the generalized second order Riccati equations, one can compute either a rational approximation of the solution or a rational solution and perform a location of the singularities in the complex plane. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

4.
    
In this paper we formulate a non‐isothermal, non‐Newtonian Hele–Shaw flow with nonlinear thermal conductivity from the injection molding. Then we study the existence of the resulting nonlinear system. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

5.
    
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   

6.
    
In this paper, we present a method for solving the Emden–Fowler equation using the Adomian polynomials and the operational calculus introduced by the authors. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

7.
    
There exists a close link between fractional systems and infinite dimensional systems described by diffusion equations. This link can be demonstrated analytically and is reminded in this article. This fractional behaviour results in fact in the system infinite dimension along with constant geometric characteristics. This article demonstrates that several other classes of differential equations also exhibit, on a frequency band, a fractional behaviour. The fractional behaviour is obtained with these equations on a space of finite dimension but with particular geometric characteristics.  相似文献   

8.
本文研究了$varrho$阶非线性Riemann-Liouville型分数阶时滞振动微分方程解的存在性和有限时间稳定性.我们采用不动点定理来研究解的存在性结果.此外,基于一些重要的不等式,我们研究了系统的有限时间稳定性.最后,通过例子验证了结论的合理性.  相似文献   

9.
10.
We obtain a system of integral equations for the spinor amplitude of a wave packet describing a massive neutral Dirac particle in a curved space–time with an arbitrary geometry. This equation permits describing the spin dynamics of fermions in gravitational fields adequately to the quantum nature of spin. We consider a specific example of the Kerr–Schild metric. We also discuss the problem of massive neutrino oscillations in an external gravitational field.  相似文献   

11.
    
An asymptotic expansion of the contrasting structure‐like solution of the generalized Kolmogorov–Petrovskii–Piskunov equation is presented. A generalized maximum principle for the pseudoparabolic equations is developed. This, together with the generalized differential inequalities method, allows to prove the consistence and convergence of the asymptotic series method. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

12.
    
In this article, the new exact travelling wave solutions of the nonlinear space‐time fractional Burger's, the nonlinear space‐time fractional Telegraph and the nonlinear space‐time fractional Fisher equations have been found. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into ordinary differential equations of integer order in the sense of the Jumarie's modified Riemann–Liouville derivative. The ‐expansion method is effective for constructing solutions to the nonlinear fractional equations, and it appears to be easier and more convenient by means of a symbolic computation system. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

13.
This paper considers time-fractional (2+1) $$ left(2+1right) $$-dimensional Wu–Zhang nonlinear system of partial differential equation describing a long dispersive wave. An approximate analytical solution of the dispersion relation of the long wave has been obtained by the fractional reduced differential transform method (FRDTM). The effect of fractional-order α $$ alpha $$ on the wave profile of the solution is discussed graphically and comparing the exact solution of Wu–Zhang equation when α=1 $$ alpha =1 $$. The result shows that the present method reveals the effectiveness, efficiency, and reliability of computed mathematical results to easily solve the fractional-order Wu–Zhang (WZ) system of differential equations.  相似文献   

14.
Following a suggestion from A. Thiaville and J. Miltat, whose work and experiments are about ferromagnetic thin layers and nanowires, we study in this paper the behaviour of the Landau–Lifschitz equation in a straight ferromagnetic wire. As the diameter of the domain and the exchange coefficient in the equation simultaneously tend to zero, we perform an asymptotic expansion to precise the solution for well‐prepared initial conditions and are led to consider 2D exterior problems. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

15.
研究一类多滞量非线性双曲型偏泛函微分方程解的振动性,借助广义Riccati变换和微分不等式技巧,获得了该类方程振动的若干新的充分条件,同时也给出了实际应用的例子.  相似文献   

16.
朱红宝 《应用数学和力学》2019,40(12):1356-1363
讨论了一类奇异摄动非线性分数阶时滞问题.首先利用奇异摄动方法求出了问题的外部解.再利用伸展变量法构造了问题在边界附近的两个边界层校正项,得出了所提问题的形式渐近解.最后,在合适的假设条件下,利用微分不等式理论证明了解的一致有效性,并给出了结论及未来的研究方向.  相似文献   

17.
    
In this paper, we establish exact solutions of the Cauchy problem for the 3D cylindrically symmetric incompressible Navier–Stokes equations and further study the global existence and asymptotic behavior of solutions. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

18.
    
In this article, the Exp‐function method is applied to nonlinear Burgers equation and special fifth‐order partial differential equation. Using this method, we obtain exact solutions for these equations. The method is straightforward and concise, and its applications are promising. This method can be used as an alternative to obtain analytical and approximate solutions of different types of nonlinear differential equations. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010  相似文献   

19.
    
It is found that there are two piecewise functions to satisfy the conditions in the impulsive fractional partial differential system (IFrPDS), which deduce that the three different equivalent integral equations of the IFrPDS given in the cited papers are inappropriate. Next, by applying two limit properties of the IFrPDS and the properties of piecewise function, the new formula of equivalent integral equation of the IFrPDS is discovered that is the integral equation with an arbitrary continuously differentiable function of t$$ t $$ on [0,c]$$ left[0,cright] $$ to reveal the non-uniqueness of the IFrPDE's solution. Finally, an example is provided to expound the computation of the equivalent integral equation of the IFrPDS.  相似文献   

20.
Using Girsanov transformation,we derive a new link from stochastic differential equations of Markovian type to nonlinear parabolic equations of Burgers-KPZ type,in such a manner that the obtained BurgersKPZ equation characterizes the path-independence property of the density process of Girsanov transformation for the stochastic differential equation.Our assertion also holds for SDEs on a connected differential manifold.  相似文献   

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