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991.
《Numerical Methods for Partial Differential Equations》2018,34(2):419-441
In this article, we study the long‐time stability and asymptotic behavior of the immersed finite element (IFE) method for the multilayer porous wall model for the drug‐eluting stents. First, with the IFE method for the spatial descretization, and the implicit Euler scheme for the temporal discretization, respectively, we deduce the global stability of fully discrete solution. Then, we investigate the asymptotic behavior of the discrete scheme which reveals that the multilayer porous wall model converges to the corresponding elliptic equation if approaches to a steady‐state in both and norms as . Finally, some numerical experiments are given to verify the theoretical predictions. 相似文献
992.
《Numerical Methods for Partial Differential Equations》2018,34(2):602-625
Motivated by the idea that staggered‐grid methods give a greater stability and give energy conservation, this article presents a new family of high‐order implicit staggered‐grid finite difference methods with any order of accuracy to approximate partial differential equations involving second‐order derivatives. In particular, we numerically analyze our new methods for the solution of the one‐dimensional acoustic wave equation. The implicit formulation is based on the plane wave theory and the Taylor series expansion and only involves the solution of tridiagonal matrix equations resulting in an attractive method with higher order of accuracy but nearly the same computation cost as those of explicit formulation. The order of accuracy of the proposal staggered formulas are similar to the methods with conventional grids for a ‐point operator: the explicit formula is th‐order and the implicit formula is th‐order; however, the results demonstrate that new staggered methods are superior in terms of stability properties to the classical methods in the context of solving wave equations. 相似文献
993.
We consider subspace iteration (or projection‐based) algorithms for computing those eigenvalues (and associated eigenvectors) of a Hermitian matrix that lie in a prescribed interval. For the case that the projector is approximated with polynomials, we present an adaptive strategy for selecting the degree of these polynomials such that convergence is achieved with near‐to‐optimum overall work without detailed a priori knowledge about the eigenvalue distribution. The idea is then transferred to the approximation of the projector by numerical integration, which corresponds to FEAST algorithm proposed by E. Polizzi in 2009. [E. Polizzi: Density‐matrix‐based algorithm for solving eigenvalue problems. Phys. Rev. B 2009; 79 :115112]. Here, our adaptation controls the number of integration nodes. We also discuss the interaction of the method with search space reduction methods. 相似文献
994.
Resonance non-positone and non-isotone problems for first order differential systems subjected to non-local boundary conditions are reduced to the non-resonance positone and isotone case by changes of variables. This allows us to prove the existence of multiple positive solutions. The theory is illustrated by two examples for which three positive numerical solutions are obtained using the Mathematica shooting program. 相似文献
995.
The aim of this article is to study the parabolic inverse problem of determination of the leading coefficient in the heat equation with an extra condition at the terminal. After introducing a new variable, we reformulate the problem as a nonclassical parabolic equation along with the initial and boundary conditions. The uniqueness and continuous dependence of the solution upon the data are demonstrated, and then finite difference methods, backward Euler and Crank–Nicolson schemes are studied. The results of some numerical examples are presented to demonstrate the efficiency and the rapid convergence of the methods. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
996.
Abstract Seabirds breeding on islands are vulnerable to introduced predators, such as rats and cats, and the removal of such predators is generally viewed as a priority for seabird conservation and restoration. However, multiple invasive mammal species interacting may generate unexpected outcomes following the removal (eradication) of one species. Generally these indirect interactions are not well understood or demonstrated. We propose and study a prey (seabird)‐mesopredator (rat)‐superpredator (cat) model, taking into account the juvenile stages in the prey population, in order to direct conservation management for seabird conservation. We give a more biologically realistic differential system than those studied before (Courchamp et al. [1999] ; Fan et al. [2005] ), in particular for long‐lived seabird species. We present a theoretical study and show existence and uniqueness of a positive solution as well as a qualitative study of the equilibria that may appear. Because standard numerical methods, usually implemented in scientific softwares, can fail to give the right biological approximations ( Anguelov et al. [2009] ), we propose a reliable algorithm that preserves most of the qualitative properties of the continuous system, using the theory of nonstandard finite difference methods. Finally, we use biologically realistic parameters available for the representative Barau's petrel (Pinet et al. [2008] ), an endemic species from Réunion island, to present numerical simulations that support the theoretical study. Cats play the major role in seabird prey population dynamics. Seasonality in seabird breeding delays but does not prevent extinction. In all scenarios, cat control (or preferably eradication) is imperative to prevent extinction of vulnerable long‐lived seabirds, like the Barau's petrel. 相似文献
997.
Hossein Aminikhah 《Numerical Methods for Partial Differential Equations》2010,26(6):1291-1299
In this article, an analytic approximation to the solution of Blasius equation is obtained by using a new modification of homotopy perturbation method. The Blasius equation is a nonlinear ordinary differential equation which arises in the boundary layer flow. The comparison with Howart's numerical solution shows that the new homotopy perturbation method is an effective mathematical method with high accuracy. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
998.
结合某市的艾滋病现状给出了相应的传染病动力学模型,研究了其平衡点的稳定性,讨论了流行病的阈值,并对不同的说服率、不同的因病死亡率、不同的传染率分别进行了数值模拟,对该市艾滋病的预防和控制给出了理论上的指导和建议. 相似文献
999.
1000.