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On the solution of a mixed nonlinear integral equation. (English) Zbl 1209.65140

Summary: We consider a mixed nonlinear integral equation of the second kind in position and time. The existence of a unique solution of this equation is discussed and proved. A numerical method is used to obtain a system of Harmmerstein integral equations of the second kind in position. Then the modified Toeplitz matrix method, as a numerical method, is used to obtain a nonlinear algebraic system. Many important theorems related to the existence and uniqueness solution to the produced nonlinear algebraic system are derived. The rate of convergence of the total error is discussed. Finally, numerical examples when the kernel of position takes a logarithmic and Carleman forms, are presented and the error estimate, in each case, is calculated.

MSC:

65R20 Numerical methods for integral equations
45G05 Singular nonlinear integral equations
45G15 Systems of nonlinear integral equations
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