عنوان مجله
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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
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چکیده
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In this paper, we investigate nonlinear functional Volterra–Urysohn integral equations,
a class of nonlinear integral equations of Volterra type. The existence and uniqueness
of the solution to the equation is proved by a technique based on the Picard iterative
method. For the numerical approximation of the solution, the Euler and trapezoidal
discretization methods are utilized which result in a system of nonlinear algebraic
equations. Using a Gronwall inequality and its discrete version, first order of convergence
to the exact solution for the Euler method and quadratic convergence for the trapezoidal
method are proved. To prove the convergence of the trapezoidal method, a new Gronwall
inequality is developed. Finally, numerical examples show the functionality of the
methods.
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