Mine Menekşe Yılmaz^*

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 287-297, 2022, DOI:10.32604/cmes.2022.017385

Abstract The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of order α. Applying the Korovkin theorem, we arrive at the convergence of the operator with the aid of moments and central moments. We determine the rate of convergence of the operator using several tools such as -functional, modulus of continuity, second modulus of continuity. We also give a type of Voronovskaya theorem for estimating error. Moreover, we investigate some results about convergence properties of the operator in a weighted space. Finally, we give numerical examples to support our theorems… More >

M.T.C. Araújo Fernandes¹, C.O. Cardoso², W.J. Mansur³

CMES-Computer Modeling in Engineering & Sciences, Vol.113, No.3, pp. 325-342, 2017, DOI:10.3970/cmes.2017.113.341

Abstract A new adaptive (automatic) time stepping algorithm, called RCA (Rate of Convergence Algorithm) is presented. The new algorithm was applied in nonlinear finite element analysis of path-dependent problems. The step size is adjusted by monitoring the estimated convergence rate of the nonlinear iterative process. The RCA algorithm is relatively simple to implement, robust and its performance is comparable to, and in some cases better than, the automatic load incrementaion algorithm existent in commercial codes. Discussions about the convergence rate of nonlinear iterative processes, an estimation of the rate and a study of the parameters of the RCA algorithm are presented.… More >