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Weak and strong convergence of an explicit iteration scheme with perturbed mapping for nonexpansive mappings
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作者 WANG Ya-qin 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2007年第12期2032-2036,共5页
In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration ... In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration scheme are established. In particular, necessary and sufficient conditions for strong convergence of this explicit iteration scheme are obtained. At last, some useful corollaries for strong convergence of this explicit iteration scheme are given. 展开更多
关键词 Nonexpansive mapping Iteration scheme with perturbed mapping Opial condition Completely continuous
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A UNIFORMLY CONVERGENT SECOND ORDER DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED SELF-ADJOINT ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM
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作者 郭雯 林鹏程 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第3期231-241,共11页
In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniform... In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme. 展开更多
关键词 exp A UNIFORMLY CONVERGENT SECOND ORDER DIFFERENCE scheme FOR A SINGULARLY perturbed SELF-ADJOINT ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM
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UNIFORM DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED LINEAR 2ND ORDER HYPERBOLIC PROBLEM WITH ZEROTH ORDER REDUCED EQUATION
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作者 苏煜城 林平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第4期301-313,共13页
In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the a... In this paper a singularly perturbed linear second order hyperbolic problem with zeroth order reduced equation is discussed. Firstly, an energy inequality of the solution and an estimate of the remainder term of the asymptotic solution are given. Then an exponentially fitted difference scheme is developed in an equidistant mesh. Finally, uniform convergence in small parameter is proved in the sense of discrete energy norm. 展开更多
关键词 UNIFORM DIFFERENCE scheme FOR A SINGULARLY perturbed LINEAR 2ND ORDER HYPERBOLIC PROBLEM WITH ZEROTH ORDER REDUCED EQUATION
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A CLASS OF VARIATIONAL DIFFERENCE SCHEMES FOR A SINGULAR PERTURBATION PROBLEM
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作者 林平 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第4期353-359,共7页
In this paper, a singularly perturbed boundary value problem for second order self-adjoint ordinary differential equation is discussed. A class of variational difference schemes is constructed by the finite element me... In this paper, a singularly perturbed boundary value problem for second order self-adjoint ordinary differential equation is discussed. A class of variational difference schemes is constructed by the finite element method. Uniform convergence about small parameter is proved under a weaker smooth condition with respect to the coefficients of the equation. The schemes studied in refs. [1], [3], [4] and [51 belong to the cllass. 展开更多
关键词 A CLASS OF VARIATIONAL DIFFERENCE schemeS FOR A SINGULAR PERTURBATION PROBLEM
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THE UNIFORMLY CONVERGENT DIFFERENCE SCHEMES FOR A SINGULAR PERTURBATION PROBLEM OF A SELFADJOINT ORDINARY DIFFERENTIAL EQUATION
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作者 林鹏程 郭雯 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第1期35-44,共10页
In this paper, we construct a class of difference schemes with fitted factors for a singular perturbation problem of a self-adjoint ordinary differential equation. Using a different method from [1], by analyzing the t... In this paper, we construct a class of difference schemes with fitted factors for a singular perturbation problem of a self-adjoint ordinary differential equation. Using a different method from [1], by analyzing the truncation errors of schemes, we give the sufficient conditions under which the solution of lite difference scheme converges uniformly to the solution of the differential equation. From this we propose several specific schemes under weaker conditions, and give much higher order of uniform convergence, and applying them to example, obtain the numerical results. 展开更多
关键词 THE UNIFORMLY CONVERGENT DIFFERENCE schemeS FOR A SINGULAR PERTURBATION PROBLEM OF A SELFADJOINT ORDINARY DIFFERENTIAL EQUATION
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A HIGH ACCURACY DIFFERENCE SCHEME FOR THE SINGULAR PERTURBATION PROBLEM OF THE SECOND-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM
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作者 王国英 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第5期465-470,共6页
In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the origi... In this paper, combining the idea of difference method and finite element method, we construct a difference scheme for a self-adjoint problem in conservation form. Its solution uniformly converges to that of the original differential equation problem with order h3. 展开更多
关键词 A HIGH ACCURACY DIFFERENCE scheme FOR THE SINGULAR PERTURBATION PROBLEM OF THE SECOND-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM
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ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE ANALYSIS 被引量:2
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作者 石磊 王学仁 《Acta Mathematica Scientia》 SCIE CSCD 1996年第3期257-264,165+266-270,共14页
A recent method for assessing the local influence is introduced by Cook(1986), in which the normal curvature of the influence graph based on the likelihood displacement is used to monitor the influence of small pertur... A recent method for assessing the local influence is introduced by Cook(1986), in which the normal curvature of the influence graph based on the likelihood displacement is used to monitor the influence of small perturbation. Since then this method has been applied to various kind of models. However, the local influence in multivariate analysis is still an unexplored area because the influence for many statistics in multivariate analysis is not convenient to handle based on the Cook's likelihood displacement. In this paper, we suggest a method with a slight modification in Cook's approach to assess the local influence of small perturbation on a certain statistic. The local influence of the perturbation on eigenvalue and eigenvector of variance-covariance matrix in theoretical and sample version is assessed, some results for the other statistics in multivariate analysis such as generalized variance, canonical correlations are studied. Finally, two examples are analysed for illustration. 展开更多
关键词 multivariate analysis normal curvature perturbation scheme local influence
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Ground-state energy of beryllium atom with parameter perturbation method 被引量:2
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作者 Feng Wu LijuanMeng 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第9期237-240,共4页
We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom's Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold pertu... We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom's Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold perturbation scheme,where the spin-spin interaction of electrons from different shells of the atom is also considered. Calculations show that the obtained ground-state energy is in satisfactory agreement with experiment. It is found that the Coulomb repulsion of the inner-shell electrons enhances the effective nuclear charge seen by the outer-shell electrons, and the shielding effect of the outer-shell electrons to the nucleus is also notable compared with that of the inner-shell electrons. 展开更多
关键词 parameter perturbation method double-fold perturbation scheme ground-state energy
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Application of the generalized body-fixed coordinate system for the wave-body interaction problem of a small-depth elastic structure in head seas
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作者 Kyeonguk Heo Masashi Kashiwagi 《Journal of Hydrodynamics》 SCIE EI CSCD 2021年第6期1255-1270,共16页
The body-fixed coordinate system is applied to the wave-body interaction problem of a small-depth elastic structure which has both rigid and elastic body motions in head waves.In the weakly non-linear assumption,the p... The body-fixed coordinate system is applied to the wave-body interaction problem of a small-depth elastic structure which has both rigid and elastic body motions in head waves.In the weakly non-linear assumption,the perturbation scheme is used and the expansion is conducted up to second-order to consider several non-linear quantities.To solve the boundary value problem,linearization is carried out based not on inertial coordinate but on body-fixed coordinate which could be accelerated by a motion of a body.At first,the main feature of the application of body-fixed coordinate system for a seakeeping problem is briefly described.After that the transformation of a coordinate system is extended to consider an elastic body motion and several physical variables are re-described in the generalized mode.It has been found that the deformation gradient could be used for the transformation of a coordinate system if several conditions are satisfied.Provided there are only vertical bending in elastic modes and the structure has relatively small depth,these conditions are generally satisfied.To calculate an elastic motion of a body,the generalized mode method is adopted and the mode shape is obtained by solving eigen-value problem of dynamic beam equation.In the boundary condition of the body-fixed coordinate system,the motion effect reflected to free-surface boundary is considered by extrapolating each mode shape to the horizontal direction from a body.At last,simple numerical tests are implemented as a validation process.The second-order hydrodynamic force of a freely floating hemisphere is first calculated in zero forward speed condition.Next,motion and added resistance of a ship with forward speed are considered at different flexibility to confirm the effect of an elastic body motion in body-fixed coordinate system. 展开更多
关键词 HYDROELASTICITY Higher-order boundary element method(HOBEM) generalized mode method perturbation scheme body-fixed coordinate system wave-body interaction
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A non-isothermal Couette slip gas flow
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作者 MILICEV Snezana S. STEVANOVIC Nevena D. 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2013年第9期1782-1797,共16页
A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers.The flow channel is formed by two plates in relative motion.Two cases are considered:(a) is... A steady plane subsonic compressible non-isothermal Couette gas flow is analyzed for moderately high and low Reynolds numbers.The flow channel is formed by two plates in relative motion.Two cases are considered:(a) isothermal walls where the temperatures of the plates are equal and constant and(b) with constant but different plate temperatures.The Knudsen number is Kn 0.1,which corresponds to the slip and continuum flow.The flow is defined by continuity,Navier-Stokes and energy continuum equations,along with the velocity slip and the temperature jump first order boundary conditions.An analytical solution for velocity and temperature is obtained by developing a perturbation scheme.The first approximation corresponds to the continuum flow conditions,while the others represent the contribution of the rarefaction effect.In addition,a numerical solution of the problems is given to confirm the accuracy of the analytical results.The exact analytical solution,for constant viscosity and conductivity is found for the isothermal walls case as well.It is shown that it is entirely a substitution to the exact numerical solution for the isothermal walls case. 展开更多
关键词 Couette gas flow NON-ISOTHERMAL slip flow analytical solution perturbation scheme
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