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On the solution of the integro-differential equation with an integral boundary condition. (English) Zbl 1297.65206

The paper is devoted to finding sufficient conditions for the existence of a continuous solution to the integro-differential equation \(x'(t) = f(t, x(t), \int_0^1 K(s,t) x(s) ds)\) subject to the nonlocal condition \(x(0) = \lambda x(1) + \int_0^1 D(s) x(s) ds\). While the uniqueness of the solution is not discussed, the authors provide a numerical solution method. This method is of an iterative nature. Each iteration step is based on sinc quadrature formula. Both the construction of the initial value of the iteration process and the precise convergence properties remain a bit unclear.

MSC:

65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
45G10 Other nonlinear integral equations
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