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101.
In this paper, the nonlinear iterative methods, which are different from the classical algorithms, to solve inverse problems are presented. Our methods by denoting some parameters and some properties of the algorithm in both noise and noiseless cases are studied. Finally, the convergence of the sequence generated by the algorithm without noise is discussed. 相似文献
102.
Le Thi Phuong Ngoc Nguyen Anh Triet Alain Pham Ngoc Dinh 《Numerical Functional Analysis & Optimization》2017,38(9):1173-1207
In this paper, we consider a wave equation with integral nonlocal boundary conditions of memory type. First, we establish two local existence theorems by using Faedo–Galerkin method and standard arguments of density. Next, we give a su?cient condition to guarantee the global existence and exponential decay of weak solutions. Finally, we present numerical results. 相似文献
103.
In this article, we propose the Gauss-Newton methods via conjugate gradient path for solving nonlinear systems. By constructing and solving a linearized model of the nonlinear systems, we obtain the iterative direction by employing the conjugate gradient path. In successive iterations, the approximate Jacobian of the nonlinear systems is updated by a Broyden formula to construct the conjugate path. The global convergence and local superlinear convergence rate of the proposed algorithms are established under some reasonable conditions. Finally, the numerical results are reported to show the effectiveness of the proposed algorithms. 相似文献
104.
The finite difference method is applied to an optimal control problem for a system governed by a nonlinear Schrödinger equation with a complex coe?cient. The optimal control problem is discretized by the finite difference method, the error estimate for the finite difference scheme is established and the convergence of difference approximations of the optimal control according to the functional is proved. 相似文献
105.
We revisit the gamma–gamma Bayesian chain-ladder (BCL) model for claims reserving in non-life insurance. This claims reserving model is usually used in an empirical Bayesian way using plug-in estimates for the variance parameters. The advantage of this empirical Bayesian framework is that allows us for closed form solutions. The main purpose of this paper is to develop the full Bayesian case also considering prior distributions for the variance parameters and to study the resulting sensitivities. 相似文献
106.
Composite generalized Laguerre spectral method for nonlinear Fokker–Planck equations on the whole line 下载免费PDF全文
Tian‐jun Wang 《Mathematical Methods in the Applied Sciences》2017,40(5):1462-1474
In this paper, we propose a composite Laguerre spectral method for the nonlinear Fokker–Planck equations modelling the relaxation of fermion and boson gases. A composite Laguerre spectral scheme is constructed. Its convergence is proved. Numerical results show the efficiency of this approach and coincide well with theoretical analysis. Some results on the Laguerre approximation and techniques used in this paper are also applicable to other nonlinear problems on the whole line. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
107.
Sturmian comparison theory for half‐linear and nonlinear differential equations via Picone identity 下载免费PDF全文
Abdullah Özbekler 《Mathematical Methods in the Applied Sciences》2017,40(8):3100-3110
In this paper, Sturmian comparison theory is developed for the pair of second‐order differential equations; first of which is the nonlinear differential equations of the form (1) and the second is the half‐linear differential equations (2) where Φα (s ) = |s |α ? 1s and α 1 > ? > α m > β > α m + 1 > ? > α n > 0. Under the assumption that the solution of 2 has two consecutive zeros, we obtain Sturm–Picone type and Leighton type comparison theorems for 1 by employing the new nonlinear version of Picone formula that we derive. Wirtinger type inequalities and several oscillation criteria are also attained for 1 . Examples are given to illustrate the relevance of the results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
108.
Nonlinear anisotropic elliptic equations in
with variable exponents and locally integrable data 下载免费PDF全文
Fares Mokhtari 《Mathematical Methods in the Applied Sciences》2017,40(6):2265-2276
In this paper, we prove existence and regularity results for weak solutions in the framework of anisotropic Sobolev spaces for a class of nonlinear anisotropic elliptic equations in the whole with variable exponents and locally integrable data. Our approach is based on the anisotropic Sobolev inequality, a smoothness, and compactness results. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
109.
On generalized Poisson–Nernst–Planck equations with inhomogeneous boundary conditions: a‐priori estimates and stability 下载免费PDF全文
Victor A. Kovtunenko Anna V. Zubkova 《Mathematical Methods in the Applied Sciences》2017,40(6):2284-2299
In this paper, we consider the strongly nonlinear Nernst–Planck equations coupled with the quasi‐linear Poisson equation under inhomogeneous, moreover, nonlinear boundary conditions. This system describes joint multi‐component electrokinetics in a pore phase. The system is supplemented by the force balance and by the volume and positivity constraints. We establish well‐posedness of the problem in the variational setting. Namely, we prove the existence theorem supported by the energy and the entropy a‐priori estimates, and we provide the Lyapunov stability of the solution as well as its uniqueness in special cases. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
110.
Heng Li Yongzhi Xu Jian‐Rong Zhou 《Mathematical Methods in the Applied Sciences》2017,40(10):3566-3579
Ductal carcinoma in situ – a special cancer – is confined within the breast ductal only. We derive the mathematical ductal carcinoma in situ model in a form of a nonlinear parabolic equation with initial, boundary, and free boundary conditions. Existence, uniqueness, and stability of problem are proved. Algorithm and illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献