[PDF] Top 20 Numerical solution of nonlinear Hammerstein integral equations by using Legendre-Bernstein basis

... The Bernstein form of a polynomial offers valuable insight into its geo- metrical behavior, and has thus won widespread acceptance as the basis for B´ ezier curves and ... See full document

... for Nonlinear Volterra—Fredholm-Hammerstein Integral Equations,” Communications in Nonlinear Sci- ence and Numerical Simulation, ... See full document

... Lane-Emden equations, the main difficulty arises in the singularity of the equation at x = ...the solution of Lane-Emden equations as well as those of a variety of nonlinear problems in quantum ... See full document

... these equations with operational ma- trices with more huge computations and opera- tion counts ...the nonlinear Fredholm integral equation to an optimal control problem and then used a linear ... See full document

... Stochastic integral equations are widely applied in engineering, biology, oceanography, physical sciences, ...Volterra integral equations do not have ex- act solutions, so it makes sense to ... See full document

... with nonlinear boundary conditions. In this paper, we consider the nonlinear Fredholm-Hammerstein integral equations and nonlinear Volterra-Hammerstein integral ... See full document

... solving nonlinear mixed Hammerstein integral ...Several numerical methods for approximating the solution of Hammerstein integral equations are ... See full document

... basis. In the following of this section, we introduce the concept of operational matrix of product. Suppose that U be a column vector and X(x) be the Bell vector which was defined in Eq. (2.2). The matrix ˆ U of ... See full document

... the solution of linear and nonlinear Volterra integral equations of the first ...on Bernstein polynomi- ...Volterra integral equa- tions of the first kind is very effective, ... See full document

... a numerical method is proposed for solving the fuzzy linear Fredholm integral equations of the second ...choose Legendre polynomials as basis functions and collocation method to ... See full document

... given integral equation into a system of non-linear equations, which has to be solved with some kind of iterative ...the solution may be evaluated analytically only in favorable cases, while in ... See full document

... solving integral equations. Since these equations usually cannot be solved explicitly, so it is required to obtain approximate ...numerous numerical methods which have been focusing on the ... See full document

... of Hammerstein integral equations has been widely studied; see for example [–] and references ...of Hammerstein integral equations of the ... See full document

... The paper is organized as follows: Some nota- tions and theorems about the structure of fuzzy sets are reviewed in Section 2. In Section 3, at first, we review two-dimensional fuzzy splines in- terpolation. Also, we ... See full document

... [7] C. Franke , R. Shaback, Solving Partial Differential Equations by collocation using Radial Basis Dunctions, Applied Mathematics and Computation, Volume 93, Issue 1 (1998) , pp. 73-82. [8] I. M. ... See full document

... How to cite this paper: Liu, Z.L. and Sun, G.Q. (2016) Gauss-Legendre Iterative Me- thods and Their Applications on Nonlinear Systems and BVP-ODEs. Journal of Applied Mathematics and Physics , 4, 2038-2046. ... See full document

... about Hammerstein-type coupled systems of integral equations, we refer [12], where, by a special cone and using fixed point index theory, Cui and Sun, inves- tigate the existence of positive ... See full document

... In this section, for confirming the accuracy of the proposed scheme in the previous section analytically, we provide an upper bound for difference between the exact solution of (1) and our approximated ... See full document

... and Legendre polynomials are well known family of orthogonal polynomials on the interval [−1,1] that have many applications and widely used because of their good properties in the approximation of ...a ... See full document

... from using Lag- (3,0) for all three types of interpolations where the spectral resolution would be limited to about 25 points per ...schemes using the Lagrange basis functions are Lag-(3,0)-(4,0)- ... See full document