Application of Fixed Point Method for Solving Nonlinear Volterra-hammerstein Integral Equation
نویسندگان
چکیده
There are various numerical methods to solve nonlinear integral equations. Most of them transform the integral equation into a system of nonlinear algebraic equations. It is cumbersome to solve these systems, or the solution may be unreliable. In this paper, we study the application of the fixed point method to solve Volterra-Hammerstein integral equations. This method does not lead to a nonlinear algebraic equations system. We show how the proper conditions guarantee the uniqueness of the solution and how the fixed point method approximates this solution. A bound for the norm of the error is derived and our results prove the convergence of the method. Finally, we present numerical examples which confirm our approach.
منابع مشابه
Legendre wavelet method for solving Hammerstein integral equations of the second kind
An ecient method, based on the Legendre wavelets, is proposed to solve thesecond kind Fredholm and Volterra integral equations of Hammerstein type.The properties of Legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known Newton's method. Examples assuring eciencyof the method and its sup...
متن کاملA new iteration method for solving a class of Hammerstein type integral equations system
In this work, a new iterative method is proposed for obtaining the approximate solution of a class of Hammerstein type Integral Equations System. The main structure of this method is based on the Richardson iterative method for solving an algebraic linear system of equations. Some conditions for existence and unique solution of this type equations are imposed. Convergence analysis and error bou...
متن کاملNumerical solution of the spread of infectious diseases mathematical model based on shifted Bernstein polynomials
The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...
متن کاملProjection-iteration Method for Solving Nonlinear Integral Equation of Mixed Type
In this paper, the existence of a unique solution of Volterra-Hammerstein integral equation of the second kind (VHIESK) is proved by using Banach fixed point theorem (BFPT) in the space ] , 0 [ ) ( 2 T C L , where represents the domain of integration of the variable space and T is the time. Then, different kinds of projectioniteration methods (PIMs) for solving this integral equation in t...
متن کاملExistence of Solutions for some Nonlinear Volterra Integral Equations via Petryshyn's Fixed Point Theorem
In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.
متن کامل