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A Fitted Numerov Method for Singularly Perturbed parabolic partial differential equation with a Small Negative Shift Arising in Control Theory

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Numerical Mathematics(Theory,Methods and Applications) 2014年第1期7卷 23-40页

作者： R.Nageshwar Rao P.Pramod Chakravarthy Department of Mathematics Visvesvaraya National Institute of TechnologyNagpur440010India

In this paper,a fitted Numerov method is constructed for a class of singularly perturbed one-dimensional parabolic partial differential equations with a small negative shift in the temporal *** boundary value problems are associated with a furnace used to process a metal sheet in control ***,the study focuses on the effect of shift on the boundary layer behavior of the solution via finite difference *** the shift parameter is smaller than the perturbation parameter,the shifted term is expanded in Taylor series and an exponentially fitted tridiagonal finite difference scheme is *** proposed finite difference scheme is unconditionally *** the shift parameter is larger than the perturbation parameter,a special type of mesh is used for the temporal variable so that the shift lies on the nodal points and an exponentially fitted scheme is *** scheme is also unconditionally *** applicability of the proposed methods is demonstrated by means of two examples.

关键词： Singular perturbations parabolic partial differential equation exponentially fitted method differential-difference equations

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A New Computational Approach for Solving Optimal Control of Linear PDEs Problem

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Acta Mathematicae Applicatae Sinica 2014年第3期30卷 735-748页

作者： M.Mahmoudi A.V.Kamyad S.Effati Department of Mathematics University of Qom Department of Mathematics Ferdowsi University of Mashhad

In this paper, we present a new computational approach for solving an internal optimal control problem, which is governed by a linear parabolic partial differential equation. Our approach is to approximate the PDE problem by a nonhomogeneous ordinary differential equation system in higher dimension. Then, the homogeneous part of ODES is solved using semigroup theory. In the next step, the convergence of this approach is verified by means of Toeplitz matrix. In the rest of the paper, the optimal control problem is solved by utilizing the solution of homogeneous part. Finally, a numerical example is given.

关键词： optimal control parabolic partial differential equation semigroups theory, nonlinear programming Toeplitz matrix

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IMPROVEMENT ON STABILITY AND CONVERGENCE OF A. D. I. SCHEMES

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Applied Mathematics and Mechanics(English Edition) 1999年第1期20卷 76-83页

作者：程爱杰 Department of Mathematics Shandong University Jinan 250100 China

Alternating direction implicit (A.D.I.) schemes have been proved valuable in the approximation of the solutions of parabolic partial differential equations in multi-dimensional space. Consider equations in the form partial derivative u/partial derivative t - partial derivative/partial derivative x(a(x,y,t) partial derivative u/partial derivative x) - partial derivative/partial derivative y(b(x,y,t) partial derivative u partial derivative y) = f Two A.D.I. schemes, Peaceman-Rachford scheme and Douglas scheme will be studied. In the literature, stability and convergence have been analysed with Fourier Method, which cannot be extended beyond the model problem with constant coefficients. Additionally, L-2 energy method has been introduced to analyse the case of non-constant coefficients, however, the conclusions are too weak and incomplete because of the so-called 'equivalence between L-2 norm and H-1 semi-norm'. In this paper, we try to improve these conclusions by H-1 energy estimating method. The principal results are that both of the two A.D.I. schemes are absolutely stable and converge to the exact solution with error estimations O(Delta t(2) + h(2)) in discrete H-1 norm. This implies essential improvement of existing conclusions.

关键词： P-R scheme Douglas scheme parabolic partial differential equation variable coefficient H-1 energy estimating method stability and convergence

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A fast local routing repair scheme for wireless mobile ad hoc network

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Science China(Information Sciences) 2011年第1期54卷 111-122页

作者： QIN DanYang,SHA XueJun & XU YuBin Electronics and Information Engineering School,Harbin Institute of Technology,Harbin 150001,China Electronics and Information Engineering School Harbin Institute of Technology Harbin China

Mobile ad hoc network(MANET)is a centerless packet radio network which does not use fixed *** has recently received tremendous attention due to its capabilities of self-configuration and ***,attenuation and interference caused by node mobility and wireless channel sharing weaken the stability of communication links.A mathematical exploring model for the next hop has been established based on the optimal exploring *** negative impact of wireless routes discontinuity has been alleviated by a novel fast local routing repair scheme(FLRRS)proposed in this paper,wherein the route requirement zone has been restricted into a pie slice region on intermediate nodes according to the solution of exploring *** scheme is an effective approach in reducing the average end-to-end delay during routing *** also allows continuous packet forwarding for fault ***-2 based simulation results showed remarkable successful packet delivery rate and end-to-end delay improvements of source-initiated routing protocol with the fast local repair scheme,especially in the case of high dynamic environments with heavy traffc loads.

关键词： FLRRS optimal exploration parabolic partial differential equation fault resilience MANET

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OSCILLATION FOR SYSTEMS OF NONLINEAR NEUTRAL TYPE parabolic partial FUNCTIONAL differential equationS

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Applied Mathematics(A Journal of Chinese Universities) 1997年第2期12卷 165-178页

作者： YANGJUN GUANXINPING DepartmentofMathematicsandPhysics YanshanUniversityQinhuangdao066004.

This paper discusses the oscillation of solutions for systems of nonlinear neutral type parabolic partial fuctional differential equations of the

关键词： parabolic partial differential equation nonlinear neutral type system oscillation

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