On the Convergence of Iterative Difference Schemes with Nonuniform Meshes for Nonlinear Parabolic Systems

ＯｎｔｈｅＣｏｎｖｅｒｇｅｎｃｅｏｆＩｔｅｒａｔｉｖｅＤｉｆｆｅｒｅｎｃｅＳｃｈｅｍｅｓｗｉｔｈＮｏｎｕｎｉｆｏｒｍＭｅｓｈｅｓｆｏｒＮｏｎｌｉｎｅａｒＰａｒａｂｏｌｉｃＳｙｓｔｅｍｓ￥（周毓麟）（沈隆钧）（袁光伟）ＺｈｏｕＹｕｌｉｎ；ＳｈｅｎＬｏｎ...     

On Some Practical Difference Schemes with Intrinsic Parallelism for Nonlinear Parabolic Systems

ＯｎＳｏｍｅＰｒａｃｔｉｃａｌＤｉｆｆｅｒｅｎｃｅＳｃｈｅｍｅｓｗｉｔｈＩｎｔｒｉｎｓｉｃＰａｒａｌｌｅｌｉｓｍｆｏｒＮｏｎｌｉｎｅａｒＰａｒａｂｏｌｉｃＳｙｓｔｅｍｓＺｈｏｕＴｈｌｉｎ（周毓麟）ＳｈｅｎＬｏｎｇｊｕｎ（沈隆钧）ａｎｄＹｕａｎＧｕａｎ...     

Existence and Uniqueness of Weak Solutions for Quasilinear Parabolic Systems

Consider the following IBVP for quasilinear parabolic systemsWhereΩis a bounded domain in R~n with a sufficiently smooth boundary(?)Ω,u=     

On Singular Solutions of Boundary Value Problems for Quasilinear Parabolic Equations with Absorption

The existence and nonexistence of non-trivial solutions for the boundary value problemare studied.     

On the Rate of Convergence of the Finite-Difference Approximations for Parabolic Bellman Equations with Constant Coefficients

The error bounds of order for two types of finite-difference approximation schemes of parabolic Bellman equations with constant coefficients are obtained, where h is x-mesh size and τ is t-mesh size. The key methods employed are the maximum principles for the Bellman equation and the approximation schemes.     

Convergence of Solutions of Nonhomogeneous Linear Difference Systems with Delays

Sufficient conditions are given for the asymptotic constancy of the solutions of a linear system of difference equations with delays. Moreover, it is shown that the limits of the solutions, as t→∞, can be computed in terms of the initial function and a special matrix solution of the corresponding adjoint equation.     

On the Convergence of Chebyshev’s Method for Multiple Polynomial Zeros

In this paper we investigate the local convergence of Chebyshev’s iterative method for the computation of a multiple polynomial zero. We establish two convergence theorems for polynomials over an arbitrary normed field. A priori and a posteriori error estimates are also provided. All of the results are new even in the case of simple zero.     

On Doubly Degenerate Quasilinear Parabolic Equations of Higher Order

We deal with the existence of periodic solutions for doubly degenerate quasilinear parabolic equations of higher order, which can degenerate, on a part of the boundary, on a segment in the interior of the domain and in time.     

Continuity of Weak Solutions for Quasilinear Parabolic Equations with Strong Degeneracy

The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form U_t-Δφ(u)=O, whereφ■C~1(R~1)is a strictly monotone increasing function.Clearly,the above equation has strong degeneracy,i.e.,the set of zero points ofφ′(·)is permitted to have zero measure. This is an answer to an open problem in[13,p.288].     

Finite Difference Method of Boundary Problem for Nonlinear Pseudo-Hyperbolic Systems

§1 In the study of the practical problems, such as the forced vibration of plane boundary layer, the transfer of the bioelectric signal in aminal nervous systems and so forth, the linear and nonlinear equations with the main part of form u_(lt)-u_(xxt) of pseudo-hyperbolic type often appear. Many authors have paid attention to solve various problems for the linear and nonlinear pseudo-hyperbolic equations. For a fairly general family of nonlinear pseudo-hyperbolic systems, which contains above mentioned equations as simple special cases, the global solutions of the periodic boundary problems and the initial problems are obtained by Galerkin's method in[7].     

On the Convergence Rate of a Space Decomposition Method

Domain decomposition method and multigrid method can be unified in the framework of the space decomposition method. This paper has obtained a new result on the convergence rate of the space decomposition method, which can be applied to some nonuniformly elliptic problems.     

On the Convergence of a Space Decomposition Method for Nonlinear Pròblems

SupportedbyNSFCproject.ContractNo.19771034TheSchwarzalternatingmethodofpartialdifferentialequationappearedonehundredyearsagoandhasbeenappliedtonumericalcomputationsince1960s.NowithasdevelopedintoSchwarzalgorithmconvenientforparallelcomputation.P.L.Lions[1]firststudiedtheSchwarzalgoritlunbyusingviewpointofspacedecomposition(seealso[2]).ThenJ.C.Xu[3]hasproposedspacedecompositionmethodtounifydomaindecompositionmethod(includingSchwarzalgorithms)andmultigridmethod.Since1990sX.C.Taihasstudie…     

Finite Volume Element Predictor-corrector Method for a Class of Nonlinear Parabolic Systems

A finite volume element predictor-corrector method for a class of nonlinear parabolic system of equations is presented and analyzed. Suboptimal L2 error estimate for the finite volume element predictor-corrector method is derived. A numerical experiment shows that the numerical results are consistent with theoretical analysis.     

A Class of Cauchy Problem for Quasilinear Hyperbolic Systems with the Weakly Dissipative Terms

ＡＣｌａｓｓｏｆＣａｕｃｈｙＰｒｏｂｌｅｍｆｏｒＱｕａｓｉｌｉｎｅａｒＨｙｐｅｒｂｏｌｉｃＳｙｓｔｅｍｓｗｉｔｈｔｈｅＷｅａｋｌｙＤｉｓｓｉｐａｔｉｖｅＴｅｒｍｓ￥ＬｉｕＦａｇｕｉ；ＹａｎｇＱｉａｏ（ＮｏｒｔｈＣｈｉｎａＩｎｓｔｉｔｕｔｅｏｆＷａｔｅ...     

Stability of Solutions for a Class of Quasilinear Degenerate Parabolic Equations

ＳｔａｂｉｌｉｔｙｏｆＳｏｌｕｔｉｏｎｓｆｏｒａＣｌａｓｓｏｆＱｕａｓｉｌｉｎｅａｒＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎｓ￥ＺｈａｏＪｕｎｎｉｎｇ（赵俊宁）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉｖｅｒｓｉｔ...     

Convergence of a Stochastic Method for the Modeling of Polymeric Fluids

We present a convergence analysis of a stochastic method for numerical modeling of complex fluids using Brownian configuration fields (BCF) for shear flows. The analysis takes into account the special structure of the stochastic partial differential equations for shear flows. We establish the optimal rate of convergence. We also analyze the nature of the error by providing its leading order asymptotics.     

Existence and Nonexistence of Global Solution for Quasilinear Parabolic Equation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ，ｗｅｓｔｕｄｙｔｈｅｅｘｉｓｔｅｎｃｅａｎｄｎｏｎｅｘｉｓｔｅｎｃｅｏｆｇｌｏｂａｌｐｏｓｉｔｉｖｅｓｏｌｕｔｉｏｎｓｏｆｔｈｅｆｏｌｌｏｗｉｎｇｑｕａｓｉｌｉｎｅａｒｐａｒａｂｏｌｉｃｅｑｕａｔｉｏｎｓｗｉｔｈｎｏｎ－ｌｉｎｅａｒｂｏｕｎｄａｒｙｃｏｎｄｉｔｉｏｎｓ：ｕｔ＝１ｍ△ｕｍ－ｕｎ，　　　ｘ∈Ω，ｔ＞０１ｍ·ｕｍγ＝ｕｐ，ｘ∈Ω，ｔ＞０（１）ｕ（ｘ，０）＝ｕ０（ｘ）＞０，ｘ∈Ω－ｗｈｅｒｅｎ，ｍ，ｐａｒｅｐｏｓｉｔｉｖｅｃｏ…     

Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems

We consider an iterative scheme for finding a common element of the set of solutions of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of N nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient and approximate proximal methods. We derive a necessary and sufficient condition for weak convergence of the sequences generated by the proposed scheme.