Abstract
For this work, the main idea is to make an adapted modification to the Newton-Kantorovich method destined to solve a nonlinear integral equations, so that by this technical method we obtain a simple application to this solution. Moreover, we compare the numerical results obtained by this method against ones obtained by another authors. This comparison showed the efficiency of this method.
Highlights
Nonlinear integral equation is an important branch in contemporary mathematics and arises many applied areas which include engineering problems, such as mechanics, physics, astronomy, biology, economics, potential theory and electrostatics (Golberg, 1990; Nadir and Gagui, 2014)
Many different methods are used to obtain the numerical solution of the nonlinear integral equations (Nadir and Rahmoune, 2007; Polyanin and Manzhirov, 2008): φ (s) − ∫Ω k (s,t,φ (t))dt = f (s), s,t ∈ Ω
For the solution of the nonlinear integral equations we present specifics conditions for the existence of this ones:
Summary
Nonlinear integral equation is an important branch in contemporary mathematics and arises many applied areas which include engineering problems, such as mechanics, physics, astronomy, biology, economics, potential theory and electrostatics (Golberg, 1990; Nadir and Gagui, 2014). Many different methods are used to obtain the numerical solution of the nonlinear integral equations (Nadir and Rahmoune, 2007; Polyanin and Manzhirov, 2008): φ (s) − ∫Ω k (s,t,φ (t))dt = f (s), s,t ∈ Ω For the solution of the nonlinear integral equations we present specifics conditions for the existence of this ones:
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