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On Newton-Kantorovich method for solving the nonlinear operator equation. (English) Zbl 1352.65652

Summary: We develop the Newton-Kantorovich method to solve the system of \(2 \times 2\) nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.

MSC:

65R20 Numerical methods for integral equations
65J15 Numerical solutions to equations with nonlinear operators
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