On the basis of Yang and Bi’s work (SIAM J Numer Anal 49, p.1602-1624), this paper discusses a discretization scheme for a sort of Steklov eigenvalue problem and proves the high effiency of the scheme. With the scheme, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. And the resulting solution can maintain an asymptotically optimal accuracy. Finally, the numerical results are provided to support the theoretical analysis..
Hyers-Ulam stability is a basic sense of stability for functional equations. In the present paper we discuss the Hyers-Ulam stability of a kind of iterative equations in the class of Lipschitz functions. By the construction of a uniformly convergent sequence of functions we prove that, for every approximate solution of such an equation, there exists an exact solution near it.
Hyers-Ulam stability is a basic sense of stability for functional equations. In the present paper we discuss the Hyers-Ulam stability of series-like iterative equations with variable coefficients. By the construction of a uniformly convergent sequence of functions we prove that if we can find a C 1 approximate solution of such an equation, then there must be a unique C 1 solution of this equation which is close to the C 1 approximate solution.
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