TY - JOUR ID - TI - Using Bernstein Polynomials Method for Solving High-order Nonlinear Volterra-Fredholm Integro Differential Equation AU - Intisar Swedain Ali PY - 2015 VL - 21 IS - 89 /علمي SP - 13 EP - 20 JO - journal of the college of basic education مجلة كلية التربية الاساسية SN - 18157467 27068536 AB -

AbstractIn this paper, the Bernstein Polynomial method is used to find an approximate solution initials values problem for high-order nonlinear Volterra Fredholm integro differential equation of the second kind. Some different examples considered and the solution discussed numerically and display graphically. By enhancing the degree of Bernstein Polynomial, we can improve the accuracy results. The simulation results were also compared with other researchers' work. 1.IntroductionIntegral and integro-differential equations play an important role in characterizing many social, biological, physical and engineering problems. Nonlinear integral and inegro-differential equations are usually hard to solve analytically and exact solutions are rather difficult to be obtained. Many numerical methods have been presented to solve this problem such as Legendre wavelets method  presented by Razzaghi and Yousefi to solve a high-order nonlinear Volterra-Fredholm integro-differential equation. Cerdik-Yaslan and Akyuz-Dascioglu  established Chebyshev Polynomial method for the solution nonlinear Fredholm-Volterra integro-differential equations. In addition, Reihani and Abadi  presented a numerical method address rationalized Haar functions method for solving Fredholm and Volterra integral equations. In fact, Araghi and Behzadi,  have solved nonlinear Volterra-Fredholm integro-differential equations by utilizing the modified Adomian decomposition method. Finally, from a recent study Yüzbasi et al.  have used a collocation approach for solving high-order linear Fredholm-Volterra integro-differential equations. ER -