New approximation methods for solving elliptic boundary value problems via Picard-Mann iterative processes with mixed errors

Boundary value problems

Heng-you Lan¹  Teng-fei Li² 

[1] Engineering, Zigong, P.R. China;College of Mathematics and Statistics, Sichuan University of Science &Institute of Nonlinear Physical Science, Sichuan University of Science &

关键词: new Picard-Mann approximation;    common fixed point;    nonexpansion and contraction;    elliptic boundary value problem;    convergence and stability;    47H10;    54H25;    47H09;   

DOI  :  10.1186/s13661-017-0914-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we introduce and study a class of new Picard-Mann iterative methods with mixed errors for common fixed points of two different nonexpansive and contraction operators. We also give convergence and stability analysis of the new Picard-Mann iterative approximation and propose numerical examples to show that the new Picard-Mann iteration converges more effectively than the Picard iterative process, Mann iterative process, Picard-Mann iterative process due to Khan and other related iterative processes. Furthermore, as an application, we explore iterative approximation of solutions for an elliptic boundary value problem in Hilbert spaces by using the new Picard-Mann iterative methods with mixed errors for contraction operators.

【 授权许可】

CC BY