University of MazandaranCaspian Journal of Mathematical Sciences (CJMS)2676-72603120140701Numerical solution of nonlinear Hammerstein integral equations by using Legendre-Bernstein basisحل عددی معادلات انتگرال همرشتاین غیرخطی با استفاده از پایه لژاندر- برنشتاین2537477ENF.MirzaeeDepartment of Mathematics, Faculty of Science, Malayer UniversityS.FathiDepartment of Mathematics, Faculty of Science, Malayer UniversityJournal Article20120225In this study a numerical method is developed to solve the Hammerstein integral <br />equations. To this end the kernel has been approximated using the leastsquares <br />approximation schemes based on Legender-Bernstein basis. The Legender <br />polynomials are orthogonal and these properties improve the accuracy of the <br />approximations. Also the nonlinear unknown function has been approximated by <br />using the Bernstein basis. The useful properties of Bernstein polynomials help <br />us to transform Hammerstein integral equation to solve a system of nonlinear <br />algebraic equations.
http://cjms.journals.umz.ac.ir/article_477_9fe4fa2b02bfbf39e4a3749fea67fbd2.pdf