共查询到20条相似文献,搜索用时 15 毫秒
1.
Spectral-Collocation Method for Volterra Delay Integro-Differential Equations with Weakly Singular Kernels 下载免费PDF全文
A spectral Jacobi-collocation approximation is proposed for Volterra delay
integro-differential equations with weakly singular kernels. In this paper, we consider
the special case that the underlying solutions of equations are sufficiently smooth. We
provide a rigorous error analysis for the proposed method, which shows that both
the errors of approximate solutions and the errors of approximate derivatives decay
exponentially in $L^∞$ norm and weighted $L^2$ norm. Finally, two numerical examples are
presented to demonstrate our error analysis. 相似文献
2.
Variation of Parameters Method for Solving System of Nonlinear Volterra Integro-Differential Equation 下载免费PDF全文
Muhammad Aslam Noor Khalida Inayat Noor Asif Waheed & Eisa Al-Said 《advances in applied mathematics and mechanics.》2012,4(2):190-204
It is well known that nonlinear integro-differential equations play vital
role in modeling of many physical processes, such as nano-hydrodynamics, drop
wise condensation, oceanography, earthquake and wind ripple in desert. Inspired
and motivated by these facts, we use the variation of parameters method for solving system of nonlinear Volterra integro-differential equations. The proposed technique is applied without any discretization, perturbation, transformation, restrictive assumptions and is free from Adomian's polynomials. Several examples are
given to verify the reliability and efficiency of the proposed technique. 相似文献
3.
Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions 下载免费PDF全文
The theory of a class of spectral methods is extended to Volterra
integro-differential equations which contain a weakly singular
kernel $(t-s)^{-\mu}$ with $0<\mu<1$. In this work, we consider the
case when the underlying solutions of weakly singular Volterra
integro-differential equations are sufficiently smooth. We provide a
rigorous error analysis for the spectral methods, which shows that
both the errors of approximate solutions and the errors of
approximate derivatives of the solutions decay exponentially in
$L^\infty$-norm and weighted $L^2$-norm. The numerical examples are
given to illustrate the theoretical results. 相似文献
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5.
We consider pricing options in a jump-diffusion model which requires solving
a partial integro-differential equation. Discretizing the spatial direction
with a fourth order compact scheme leads to a linear system of ordinary
differential equations. For the temporal direction, we utilize the favorable
boundary value methods owing to their advantageous stability properties. In
addition, the resulting large sparse system can be solved rapidly by the
GMRES method with a circulant Strang-type preconditioner. Numerical results
demonstrate the high order accuracy of our scheme and the efficiency of the
preconditioned GMRES method. 相似文献
6.
利用谱方法和FFT技术对等离子体中带电粒子输运Fokker-Planck-Landau方程进行数值求解,研究空间均匀条件下粒子相空间分布函数随时间的演化.数值计算表明,所用计算格式能够很好地满足粒子数、动量和能量守恒要求,FFT技术的采用也使得运算工作量大为降低. 相似文献
7.
In this paper, based on a new more general ansatz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order. 相似文献
8.
ZHANG Xiao-Ling WANG Jing ZHANG Hong-Qing 《理论物理通讯》2006,46(5):779-786
In this paper, based on a new more general ansitz, a new algebraic method, named generalized Riccati equation rational expansion method, is devised for constructing travelling wave solutions for nonlinear evolution equations with nonlinear terms of any order. Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recovers the results by most known algebraic methods, but also provides new and more general solutions. We choose the generalized Burgers-Fisher equation with nonlinear terms of any order to illustrate our method. As a result, we obtain several new kinds of exact solutions for the equation. This approach can also be applied to other nonlinear evolution equations with nonlinear terms of any order. 相似文献
9.
Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations 下载免费PDF全文
In this paper, we prove the convergence of homotopy analysis method (HAM).
We also apply the homotopy analysis method to obtain approximate
analytical solutions of systems of the second kind Volterra integral equations.
The HAM solutions contain an auxiliary parameter
which provides a convenient way of controlling the convergence region
of series solutions. It is shown that the solutions obtained by the
homotopy-perturbation method (HPM) are only special cases of the HAM
solutions. Several examples are given to illustrate
the efficiency and implementation of the method. 相似文献
10.
Collocation Methods for a Class of Volterra Integral Functional Equations with Multiple Proportional Delays 下载免费PDF全文
Kai Zhang & Jie Li 《advances in applied mathematics and mechanics.》2012,4(5):575-602
In this paper, we apply the collocation methods to a class of
Volterra integral functional equations with multiple proportional
delays (VIFEMPDs). We shall present the existence, uniqueness and
regularity properties of analytic solutions for this type of equations,
and then analyze the convergence orders of the collocation solutions
and give corresponding error estimates. The numerical results verify
our theoretical analysis. 相似文献
11.
In this short paper, bilinear form of a negative order AKNS equation
is given. The N-soliton solutions are obtained through Hiorta's direct method. 相似文献
12.
用庞加莱球法测量二阶偏振模色散 总被引:3,自引:2,他引:3
用庞加莱球法测量单模光纤中的二阶偏振模色散,并对二阶偏振模色散的各个分量的统计特性及其影响进行了分析。对75km的G.652普通单模光纤的二阶偏振模色散进行了测量,并对二阶偏振模色散的平行分量、垂直分量、偏振相关色散和消偏振项进行了详细的分析.得到了二阶偏振模色散随波长的分布情况、统计特性以及偏振主态随波长的变化情况。从统计结果可以得到.与偏振相关色散项相比,消偏振项在二阶偏振模色散中起主要作用。该研究对二阶偏振模色散的补偿有一定的指导意义。 相似文献
13.
In this paper, bilinear form of a negative order AKNS equation hierarchy is given. The soliton solutions are obtained through Hiorta's direct method. 相似文献
14.
In this paper, bilinear form of a negative order AKNS equation hierarchy is given. The soliton solutions are obtained through Hiorta's direct method. 相似文献
15.
提出以电调谐的声光滤光器作为色散元件,研究光电倍增管光谱特性新的测试方法,采用时间相移技术,对系统定标,使监控光束直接截取自测量光束, 相似文献
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A Priori Error Estimates of Finite Element Methods for Linear Parabolic Integro-Differential Optimal Control Problems 下载免费PDF全文
Wanfang Shen Liang Ge Danping Yang & Wenbin Liu 《advances in applied mathematics and mechanics.》2014,6(5):552-569
In this paper, we study the mathematical formulation for an optimal
control problem governed by a linear parabolic integro-differential
equation and present the optimality conditions. We then set up its
weak formulation and the finite element approximation scheme. Based
on these we derive the a priori error estimates for its finite
element approximation both in $H^1$ and $L^2$ norms. Furthermore, some numerical tests are presented to
verify the theoretical results. 相似文献
20.
Xue-Nian Cao Jiang-Li Fu & Hu Huang 《advances in applied mathematics and mechanics.》2012,4(6):848-863
In this paper, a new numerical algorithm
for solving the time fractional Fokker-Planck equation is proposed. The
analysis of local truncation error and the stability of this method are
investigated. Theoretical analysis and numerical experiments show that
the proposed method has higher order of accuracy for solving the
time fractional Fokker-Planck equation. 相似文献