SPLINE COLLOCATION FOR FREDHOLM AND VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

Subject Areas : International Journal of Mathematical Modelling & Computations

Nehzat Ebrahimi ¹ , Jalil Rashidinia ²

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Received: 2016-04-15 Accepted : 2016-04-15 Published : 2014-03-21

Keywords: Cubic B-spline, Convergence analysis, Fredholm and Volterra integro-differential equations, Newton-Cotes formula,

Abstract :

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toillustrate the efficiency of the proposed method which shows that our method can be applied for largevalues of N. The results are compared with the results obtained by other methods to illustrate the accuracyand the implementation of our method.