𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Toeplitz matrix method and nonlinear integral equation of Hammerstein type

✍ Scribed by M.A. Abdou; M.M. El-Borai; M.M. El-Kojok

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
548 KB
Volume
223
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

The existence and uniqueness solution of the nonlinear integral equation of Hammerstein type with discontinuous kernel are discussed. The normality and continuity of the integral operator are proved. Toeplitz matrix method is used, as a numerical method, to obtain a nonlinear system of algebraic equations. Also, many important theorems related to the existence and uniqueness of the produced algebraic system are derived. Finally, numerical examples, when the kernel takes a logarithmic and Carleman forms, are discussed and the estimate error, in each case, is calculated.

πŸ“œ SIMILAR VOLUMES

Solution of nonlinear integral equations
Solution of nonlinear integral equations of Hammerstein type
✍ C.E. Chidume; E.U. Ofoedu πŸ“‚ Article πŸ“… 2011 πŸ› Elsevier Science 🌐 English βš– 223 KB

Let E be a 2-uniformly real Banach space and F , K : E β†’ E be nonlinear-bounded accretive operators. Assume that the Hammerstein equation u + KFu = 0 has a solution. A new explicit iteration sequence is introduced and strong convergence of the sequence to a solution of the Hammerstein equation is pr

Secant-like methods for solving nonlinea
Secant-like methods for solving nonlinear integral equations of the Hammerstein type
✍ M.A. HernΓ‘ndez; M.J. Rubio; J.A. Ezquerro πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 95 KB

We consider a one-parametric family of secant-type iterations for solving nonlinear equations in Banach spaces. We establish a semilocal convergence result for these iterations by means of a technique based on a new system of recurrence relations. This result is then applied to obtain existence and