Numerical Treatment of the Nonlocal Solution of Hammerstein –Volterra Integral Equation with Continuous Kernels

M. M. El- Kojok
2017 International Journal of Advanced Research in Computer Science and Software Engineering  
In this paper, the existence of a unique solution of Hammerstein -Volterra integral equation (H-VIE) of the second kind is considered and proved, under certain conditions, using Banach fixed point theorem. Moreover, a suitable numerical method, Collocation method, is used to reduce the H-VIE to a nonlocal nonlinear algebraic system (nonlocal NAS). The existence of a unique solution of the nonlocal NAS is considered. Many numerical results are calculated, when the nonlocal term is neglected in
more » ... m is neglected in the linear case and in the nonlinear case, and the error estimate, in each case, is computed. In addition, some special cases are derived and computed, in this work, when the memory takes different cases. Key Wards: Nonlocal Hammerstein -Volterra integral equation, Banach fixed point theorem, Collocation method, nonlocal nonlinear algebraic system.
doi:10.23956/ijarcsse/v7i3/01311 fatcat:2qeyisosr5cbvdivrq4fro53ia