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101.
102.
Models involving maximal monotone term and history (delay) term are considered in a mathematical and numerical point of view. 相似文献
103.
Chen Chunhua Lu Xuanzhu 《Annals of Differential Equations》2005,21(3):250-255
In this paper, a time fractional advection-dispersion equation is considered. From the relationship between the Caputo derivative and the Grunwald derivative, the Caputo derivative is approximated by using the Griinwald derivative. An implicit difference approximation for this equation is proposed. We prove that this approximation is unconditionally stable and convergent. Finally, numerical examples are given. 相似文献
104.
A variety of theorems and properties of nonlinear DAEs were discussed in part I. This paper illustrates many of these ideas
within the context of analyzing a specific nonlinear system that exhibits a variety of interesting features.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
105.
W. Bian 《Journal of Optimization Theory and Applications》2006,129(2):277-292
Sufficient conditions are given for a mapping to be γ-G inverse differentiable. Constrained implicit function theorems for
γ-G inverse differentiable mappings are obtained, where the constraint is taken to be either a closed convex cone or a closed
subset. A theorem without assuming the γ-G inverse differentiability in a finite-dimensional space is also presented.
Communicated by F. A. Potra
The author thanks the referees for valuable suggestions concerning the presentation of this paper. He also thanks Professor
J. R. L. Webb and Dr. M. French for help. 相似文献
106.
In design optimization and parameter identification, the objective, or response function(s) are typically linked to the actually independent variables through equality constraints, which we will refer to as state equations. Our key assumption is that it is impossible to form and factor the corresponding constraint Jacobian, but one has instead some fixed-point algorithm for computing a feasible state, given any reasonable value of the independent variables. Assuming that this iteration is eventually contractive, we will show how reduced gradients (Jacobians) and Hessians (in other words, the total derivatives) of the response(s) with respect to the independent variables can be obtained via algorithmic, or automatic, differentiation (AD). In our approach the actual application of the so-called reverse, or adjoint differentiation mode is kept local to each iteration step. Consequently, the memory requirement is typically not unduly enlarged. The resulting approximating Lagrange multipliers are used to compute estimates of the reduced function values that can be shown to converge twice as fast as the underlying state space iteration. By a combination with the forward mode of AD, one can also obtain extra-accurate directional derivatives of the reduced functions as well as feasible state space directions and the corresponding reduced or projected Hessians of the Lagrangian. Our approach is verified by test calculations on an aircraft wing with two responses, namely, the lift and drag coefficient, and two variables, namely, the angle of attack and the Mach number. The state is a 2-dimensional flow field defined as solution of the discretized Euler equation under transonic conditions. 相似文献
107.
A five-stage fifth-order singly diagonally implicit Runge–Kutta–Nyström method for the integration of second order differential equations possessing an oscillatory solution, is presented in this article. This method is P-stable, which is recommended for problems with a theoretical solution consisting of a periodic part of moderate frequency with a high frequency oscillation with small amplitude superimposed. It also attains an order which is one higher than existing methods of this type. Numerical comparisons with existing methods of this type show its clear advantage. 相似文献
108.
The nonsymmetric Lanczos method has recently received significant attention as a model reduction technique for large-scale systems. Unfortunately, the Lanczos method may produce an unstable partial realization for a given, stable system. To remedy this situation, unexpensive implicit restarts are developed which can be employed to stabilize the Lanczos generated model.This work was supported in part by ARPA (US Army ORA4466.01), by ARPA (Grant 60NANB2D1272), by the Department of Energy (Contract DE-FG0f-91ER25103) and by the National Science Foundation (Grants CCR-9209349 and CCR-9120008). 相似文献
109.
This paper presents a two-dimensional model for the analysis of the pressure transient of a two-phase homogeneous bubbly mixture flowing in a pipeline and the numerical integration using the centre implicit method (CIM). Experiments were conducted to confirm the proposed sonic speed equation of an air–water mixture for an air concentration of less than 1%. The 2D CIM model is compared with the method of characteristics (MoC) for a two-phase bubbly flow in a pipeline. The comparisons show that the proposed 2D CIM model generally gives good agreement with the method of characteristics. 相似文献
110.
R. K. Mohanty Samir Karaa Urvashi Arora 《Numerical Methods for Partial Differential Equations》2007,23(3):640-651
This article develops a new two‐level three‐point implicit finite difference scheme of order 2 in time and 4 in space based on arithmetic average discretization for the solution of nonlinear parabolic equation ε uxx = f(x, t, u, ux, ut), 0 < x < 1, t > 0 subject to appropriate initial and Dirichlet boundary conditions, where ε > 0 is a small positive constant. We also propose a new explicit difference scheme of order 2 in time and 4 in space for the estimates of (?u/?x). The main objective is the proposed formulas are directly applicable to both singular and nonsingular problems. We do not require any fictitious points outside the solution region and any special technique to handle the singular problems. Stability analysis of a model problem is discussed. Numerical results are provided to validate the usefulness of the proposed formulas. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献