Existence of at least one solution of singular Volterra-Hammerstein integral equation and its numerical solution

African Journal of Mathematics and Computer Science Research

R. T. Matoog¹ 

关键词: Volterra- Hammerstein integral equation;    nonlinear algebraic system (NAS);    singular kernel;    Toeplitz matrix method;    Hö;    lder inequality.;   

DOI  :  10.5897/AJMCSR2016.0660

学科分类：计算机科学（综合）

来源: Academic Journals

【 摘 要 】

In this paper, we prove the existence of at least one solution for Volterra- Hammerstein integral equation (V-HIE) of the second kind, under certain conditions, in the space, Ω is the domain of integration and T is the time. The kernel of Hammerstein integral term has a singularity, while the kernel of Volterra is continuous in time. Using a quadratic numerical method with respect to time, we have a system of Hammerstein integral equations (SHIEs) in position. The existence of at least one solution for the SHIEs is considered and discussed. Moreover, using Toeplitz matrix method (TMM), the SHIEs are transformed into a nonlinear algebraic system (NAS). Many theorems related to the existence of at least one solution for this system are proved. Finally, numerical results and the estimate error of it are calculated and computed using Mable 12.

【 授权许可】

CC BY