共查询到20条相似文献,搜索用时 15 毫秒
1.
Zeng Liu-chuan 《应用数学和力学(英文版)》2002,23(6):686-693
The convergence of theIshikawa iteration sequences with errors for constructing solutions of m-accretive operator equations
is characterized. Moreover, the error estimates of approximate solutions for locally Lipschitzian and m-accretive operator
equations are established.
Foundation items: the National Natural Science Foundation of China (19801023); the Teaching and Research Award Fund for Outstanding Young
Teachers in Higher Education Institutions of MOE, China
Biography: ZENG Liu-chuan (1965-), Professor 相似文献
2.
In this paper, a new notion of a generalized H-η-accretive operator is introduced and studied, which provides a unifying framework for the generalized m-accretive operator and the H-η-monotone operator in Banach spaces. A resolvent operator associated with the generalized H-η-accretive operator is defined, and its Lipschitz continuity is shown. As an application, the solvability for a class of variational inclusions involving the generalized H-η-accretive operators in Banach spaces is considered. By using the technique of the resolvent mapping, an iterative algorithm for solving the variational inclusion in Banach spaces is constructed. Under some suitable conditions, it is proven that the solution for the variational inclusion and the convergence of the iterative sequence generated by the algorithm exist. 相似文献
3.
Operator splitting is often used for solving advection-dispersion-reaction (ADR) equations. Each operator can be solved separately
using an algorithm appropriate to its mathematical behavior. Although a lot of research has been done in operator splitting
for solving ADR equations, numerical approaches for the reaction operator are computationally expensive. To meet the convergence
criteria of ODE (ordinary differential equation) or DAE (differential algebraic equation) solvers, a transport time step has
to be subdivided into a large number of reaction time steps. Additional computation effort is also required to reduce the
splitting error. In this paper, we develop exact solutions of various first-order reaction networks for the reaction operator
and couple those solutions with numerical solutions of the transport operator. The reactions are treated as local phenomena
and simulated using exact solutions that we develop, while advection and dispersion are treated as global processes and simulated
numerically. The proposed method avoids the numerical error from the reaction operator and requires a single-step calculation
to solve the reaction operator. Compared to conventional operator-splitting methods, the proposed method offers both computational
efficiency and simulation accuracy. 相似文献
4.
V. F. Zhuravlev 《Nonlinear Oscillations》2011,13(4):558-568
We consider linear boundary-value problems for operator equations with generalized invertible operators in Banach spaces that
have bases. Using the technique of generalized inverse operators applied to generalized invertible operators in Banach spaces,
we establish conditions for the solvability of linear boundary-value problems for these operator equations and obtain formulas
for the representation of their solutions. We consider special cases of these boundary-value problems, namely, so-called n- and d-normally solvable boundary-value problems as well as normally solvable problems for Noetherian operator equations. 相似文献
5.
A simple characteristic equation solution strategy for deriving the fundamental analytical solutions of 3D isotropic elasticity is proposed. By calculating the determinant of the differential operator matrix obtained from the governing equations of 3D elasticity, the characteristic equation which the characteristic general solution vectors must satisfy is established. Then, by substitution of the characteristic general solution vectors, which satisfy various reduced characteristic equations, into various reduced adjoint matrices of the differential operator matrix, the corresponding fundamental analytical solutions for isotropic 3D elasticity, including Boussinesq-Galerkin (B-G) solutions, modified Papkovich-Neuber solutions proposed by Min-zhong WANG (P-N-W), and quasi HU Hai-chang solutions, can be obtained. Furthermore, the independence characters of various fundamental solutions in polynomial form are also discussed in detail. These works provide a basis for constructing complete and independent analytical trial functions used in numerical methods. 相似文献
6.
用奇异函数建立非单一材质的n级阶梯形闭口薄壁杆约束扭转自由振动和强迫振动的微分方程并求得其通解,用W算子给出主振型函数的表达式及常见支承条件下杆的频率方程。 相似文献
7.
8.
Hans Engler 《Archive for Rational Mechanics and Analysis》1991,113(1):1-38
Global weak solutions of scalar second-order quasilinear hyperbolic integro-differential equations with singular kernels are constructed. Perturbations of rest states are shown to propagate with finite speed, smoothing effects of the solution operator are exhibited, and conditions for the asymptotic stability of rest states are given. The equations arise in viscoelasticity. 相似文献
9.
Constructions of the general solution for a system of partial differential equations with variable coefficients 总被引:2,自引:0,他引:2
Solving partial differential equations has not only theoretical significance,but alsopractical value.In this paper.by the property of conjugate operator.we give a method toconstruct the general solutions of a system of partial differential equations. 相似文献
10.
In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations. 相似文献
11.
E. V. Rozhkova 《Mechanics of Solids》2018,53(1):33-44
A solution of the equations of motion of a 3D anisotropic elastic medium without determining the roots of the determinant (secular) equation is obtained by a recursive operator method. A relationship between such solutions and classical solutions is established. The possibility of solving initial–boundary value problems for plane waves is considered. An example and comparative graphs of the solutions are given. 相似文献
12.
Yang Zuosheng 《国际流体数值方法杂志》1998,28(3):565-568
A complete boundary integral formulation for incompressible Navier–Stokes equations with time discretization by operator splitting is developed using the fundamental solutions of the Helmholtz operator equation with different order. The numerical results for the lift and the drag hysteresis associated with a NACA0012 aerofoil oscillating in pitch show good agreement with available experimental data. © 1998 John Wiley & Sons, Ltd. 相似文献
13.
Reza Djeddi Kivanc Ekici 《International Journal of Computational Fluid Dynamics》2016,30(7-10):495-515
A new pseudo-spectral operator is developed for time-spectral harmonic balance solutions of periodic unsteady flows. The method utilises a mechanism similar to sigma-approximation technique with Lanczos filtering function that alters the inverse of the discrete Fourier transformation matrix, leading to a modified pseudo-spectral operator. The modified operator is then used instead of the original operator that mimics the time-derivative term of the unsteady governing equations. The modified operator is capable of damping high-frequency nonlinearities in the harmonic balance solution, thus alleviating the effects of high-frequency oscillations that result in Gibbs-type phenomena. The effectiveness and robustness of the technique are demonstrated through various test cases. 相似文献
14.
In this paper, we focus on the need to solve chaotic solutions of high-dimensional nonlinear dynamic systems of which the
analytic solution is difficult to obtain. For this purpose, a Differential Control Method (DCM) is proposed based on the Mechanized
Mathematics-Wu Elimination Method (WEM). By sampling, the computer time of the differential operator of the nonlinear differential
equation can be substituted by the differential quotient of solving the variable time of the sample. The main emphasis of
DCM is placed on substituting the differential quotient of a small neighborhood of the sample time of the computer system
for the differential operator of the equations studied. The approximate analytical chaotic solutions of the nonlinear differential
equations governing the high-dimensional dynamic system can be obtained by the method proposed. In order to increase the computational
efficiency of the method proposed, a thermodynamics modeling method is used to decouple the variable and reduce the dimension
of the system studied. The validity of the method proposed for obtaining approximate analytical chaotic solutions of the nonlinear
differential equations is illustrated by the example of a turbo-generator system. This work is applied to solving a type of
nonlinear system of which the dynamic behaviors can be described by nonlinear differential equations. 相似文献
15.
周之虎 《应用数学和力学(英文版)》1994,15(3):235-246
In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s sequence convergence.After turning ageneral variable coefficient linear difference equation of order n into a set of operatorequations.we can obtain the solutions of the general n-th order variable coefficientlinear difference equation. 相似文献
16.
王凡彬 《应用数学和力学(英文版)》2000,21(11):1338-1340
Therearemanydocumentsthatdiscussblow_upofthesolutionsfortheinitial_boundaryvlueproblemsofthenonlinearSchr dingerequations,suchaspaper [1 ] .Butthepaper [1 ]hasoneweakpoint,thatis,itcannotunitediscussionforblow_upofthesolutionsfortheinitial_boundaryvalueprobl… 相似文献
17.
Yang Zuosheng 《国际流体数值方法杂志》2005,47(12):1423-1430
A complete boundary integral formulation for compressible Navier–Stokes equations with time discretization by operator splitting is developed using the fundamental solutions of the Helmholtz operator equation with different order. The numerical results for wall pressure and wall skin friction of two‐dimensional compressible laminar viscous flow around airfoils are in good agreement with field numerical methods. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
18.
张英世 《应用数学和力学(英文版)》1999,20(5):568-578
IntroductionMuchfamiliarinengineeringareelasticfoundationplates,suchasfoundationbaseplatesincivilengineering,highwaysurface,r... 相似文献
19.
I.IntroductionUsedextensivelyillengineeringareone-wayrectallgularsteppedthinplates.suchaslongandnarrow"platesofl'Oundationbaseincivilengineering,high-c"a}'surface.retainingwall,undergroundstructurefi-ame,baseplatesofsluice.shipyardando\-ertlowdam.Theyshouldnotonlymeetrequirementsofstrength,stiffnessalldsteadinessofstructuresbutalsosavematerialstotileftlll.Thus,steppedstructuresarecolnmonl}'adoptedinengineerings.Sofar.vibratio,nsofsuChplateshavenotbeendiscussedinanyliterature.Inthispaper.disc… 相似文献
20.
Fractal First-Order Partial Differential Equations 总被引:1,自引:0,他引:1
The present paper is concerned with semi-linear partial differential equations involving a particular pseudo-differential
operator. It investigates both fractal conservation laws and non-local Hamilton–Jacobi equations. The idea is to combine an
integral representation of the operator and Duhamel's formula to prove, on the one hand, the key a priori estimates for the scalar conservation law and the Hamilton–Jacobi equation and, on the other hand, the smoothing effect of
the operator. As far as Hamilton–Jacobi equations are concerned, a non-local vanishing viscosity method is used to construct
a (viscosity) solution when existence of regular solutions fails, and a rate of convergence is provided. Turning to conservation
laws, global-in-time existence and uniqueness are established. We also show that our formula allows us to obtain entropy inequalities
for the non-local conservation law, and thus to prove the convergence of the solution, as the non-local term vanishes, toward
the entropy solution of the pure conservation law. 相似文献