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Abstract: In the present paper we study the approximate solutions of a certain difference-differential equation under the given initial conditions. The well known Gronwall-Bellman integral inequality is used to establish the results. Applications to a Volterra type difference-integral equation are also given.
AMSclassification: primary 34K10; secondary 34K40.
Keywords: approximation of solutions, difference-differential equation, Gronwall-Bellman, integral inequality, Volterra type, difference-integral equation, estimate, closeness of solutions.