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131.
Andreas Rößler 《BIT Numerical Mathematics》2006,46(1):97-110
A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance. 相似文献
132.
Hideshi Yamane 《Proceedings of the American Mathematical Society》2006,134(11):3353-3361
We study the lifespan of solutions to fully nonlinear Cauchy problems with small real- or complex-analytic data. Our proofs are based on the method of majorants and the fixed point theorem for a contraction mapping.
133.
Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions 总被引:5,自引:2,他引:3
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Yi ZHOU 《数学年刊B辑(英文版)》2007,28(2):205-212
In this paper, the author considers the Cauchy problem for semilinear wave equations with critical exponent in n≥4 space dimensions. Under some positivity conditions on the initial data, it is proved that there can be no global solutions no matter how small the initial data are. 相似文献
134.
Instability of Solitary Waves in Nonlinear Composite Media 总被引:1,自引:0,他引:1
Ye Zhao 《应用数学学报(英文版)》2007,23(2):311-318
In this paper,we investigate a class of Hamiltonian systems arising in nonlinear composite media.By detailed analysis and computation we obtain a decaying estimates on the semigroup and prove the orbitalinstability of two families of explicit solitary wave solutions (slow family in anisotropic case and solitary wavesin isotropic case),which theoretically verify the related guess and numerical results. 相似文献
135.
In the present paper, we study the rate of convergence in simultaneous approximation for the Bézier variant of the Baskakov-Beta operators by using the decomposition technique of functions of bounded variation. 相似文献
136.
The mechanism of X-ray waveguide-resonance propagation or the radiation superstream model, which can become the ground of X-ray nanophotonics, is discussed briefly. Some attention is devoted to features consideration of the simplest devices characterized by the waveguide-resonance transportation of X-ray beams. The experimental data showing the user possibilities of a simplest waveguide-resonators application for diffractometry are presented. We discuss the main reasons to improve the metrological characteristics for total reflection X-ray fluorescence (TXRF) analytical method in case when the target exciting beam is formed by a waveguide-resonator. Some problems appearing during the waveguide-resonator application are formulated. 相似文献
137.
Xin Tao YE Chong LI 《数学学报(英文版)》2007,23(1):65-76
The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided. 相似文献
138.
Two different problems are proposed as approximations of the usual system modelling natural convection under the Oberbeck-Boussinesq assumptions. The error is evaluated by means of the norm of its gradient in the Hilbert space. The average Nusselt number is also estimated. 相似文献
139.
Andreas Rößler 《BIT Numerical Mathematics》2007,47(3):657-680
The weak approximation of the solution of a system of Stratonovich stochastic differential equations with a m–dimensional Wiener process is studied. Therefore, a new class of stochastic Runge–Kutta methods is introduced. As the main
novelty, the number of stages does not depend on the dimension m of the driving Wiener process which reduces the computational effort significantly. The colored rooted tree analysis due
to the author is applied to determine order conditions for the new stochastic Runge–Kutta methods assuring convergence with
order two in the weak sense. Further, some coefficients for second order stochastic Runge–Kutta schemes are calculated explicitly.
AMS subject classification (2000) 65C30, 65L06, 60H35, 60H10 相似文献
140.
In general, we will use the numerical differentiation when dealing with the differential equations. Thus the differential equations can be transformed into algebraic equations and then we can get the numerical solutions. But as we all have known, the numerical differentiation process is very sensitive to even a small level of errors. In contrast it is expected that on average the numerical integration process is much less sensitive to errors. In this paper, based on the Sinc method we provide a new method using Sinc method incorporated with the double exponential transformation based on the interpolation of the highest derivatives (SIHD) for the differential equations. The error in the approximation of the solution is shown to converge at an exponential rate. The numerical results show that compared with the exiting results, our method is of high accuracy, of good convergence with little computational efforts. It is easy to treat nonhomogeneous mixed boundary condition for our method, which is unlike the traditional Sinc method. 相似文献