SPLINE COLLOCATION FOR NONLINEAR FREDHOLM INTEGRAL EQUATIONS

Subject Areas : International Journal of Mathematical Modelling & Computations

Z. Mahmoodi ¹ , J. Rashidinia ² , E. Babolian ³

1 - Science and Research Branch, Islamic Azad University, Tehran, Iran Iran, Islamic Republic of Department of Mathematics
2 - Science and Research Branch, Islamic Azad University, Tehran, Iran Iran, Islamic Republic of Department of Mathematics
3 - Science and Research Branch, Islamic Azad University, Tehran, Iran Iran, Islamic Republic of Department of Mathematics

Received: 2016-04-12 Accepted : 2016-04-12 Published : 2011-12-22

Keywords: Nonlinear Fredholm integral equation, Cubic B-spline, Newton-Cotes, Collocation, Convergence analysis,

Abstract :

The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented method is tested with four examples, and the errors in the solution are compared with the existing methods [1, 2, 3, 4] to verify the accuracy and convergent nature of proposed methods. The RMS errors in the solutions are tabulated in table 3 which shows that our method can be applied for large values of n, but the maximum n which has been used by the existing methods are only n = 10, moreover our method is accurate and stable for different values of n.