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Abstract In the current paper, an error estimate has been proposed to find a second-order finite difference scheme for solving the Riesz space distributed-order diffusion equation. The convergence order of the proposed method is O (τ 2 + h 2). The numerical results show the efficiency of the new technique. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we defined the scattering energy intensity based on the Poynting vector to quantitatively study the cloak effect of electromagnetic waves in the time domain. The influences of the effective working frequency bands of four kinds of electromagnetic cloak materials, incidence angle of electromagnetic waves and the number of approximately cloak layers on the cloak effect are studied. To the best of our knowledge, this is the first time to use the time domain method to quantitatively study the effective working frequency band and the scattering energy intensity of cloak materials. [ABSTRACT FROM AUTHOR]

Abstract: A modified Rayleigh conjecture (MRC) in scattering theory was proposed and justified by the author [A.G. Ramm, Modified Rayleigh conjecture and applications, J. Phys. A 35 (2002) L357–L361]. The MRC allows one to develop efficient numerical algorithms for solving boundary-value problems. It gives an error estimate for solutions. In this paper the MRC is formulated and proved for static problems. [Copyright &y& Elsevier]

Abstract: This paper proposes a rank-one modified fitting algorithm. The main feature of the approach is that the update formula for the deflection matrix in an iteration is deduced from a quadratic fitting function, not from the traditional quasi-Newton equation. Under some mild assumptions, the algorithm is globally and linearly convergent. [Copyright &y& Elsevier]

In this paper, we consider the problem of best approximation in lp (n), 1 ≤ p ≤ ∞. If hp, 1 ≤ p < ∞, denotes the best lp-approximation of the element h ∊ rn from a proper affine subspace K of rn, h ∉ K, then limp→1 hp = h1&ast;, where h1&ast;, is a best l1-approximation of h from K, the so-called natural best k1-approximation. We prove that, for every r ∊ n, the best kp-approximations have a Taylor expansion of order r of the form hp=h1&ast;+∑lower limit l=1, upper limit r αl(p−1)l+γp(r) for some αl ∊ rn, 1 ≤ l ≤ r, and γp(r) ∊ rn with &z.sfnc;γp(r)&z.sfnc;=o((p−1)r+1). [Copyright &y& Elsevier]

In this paper, we develop a new iterative algorithm for solving a class of nonlinear mixed implicit variational inequalities and give the convergence analysis of the iterative sequences generated by the algorithms. In our results, we do not assume that the mapping is strongly monotone, nor do we assume that the mapping is surjective. [Copyright &y& Elsevier]