Abstract
In this paper, we introduce a new scheme based on the exponential spline function for solving linear second-order Fredholm integro-differential equations. Our approach consists of reducing the problem to a set of linear equations. We prove the convergence analysis of the method applied to the solution of integro-differential equations. The method is described and illustrated with numerical examples. The results reveal that the method is accurate and easy to apply. Moreover, results are compared with the method in (J. Comput. Appl. Math. 290:633–640, 2015).
Highlights
Integro-differential equations have gained a lot of interest in multitude of uses, in sciences related to nature and engineering
A few of these solutions are as follows: approximate solution that is obtained by using spline functions [1], Jacobi-spectral method for integro-delay differential equations with weakly singular kernels [25], polynomial spline functions that have free boundary condition for solving the first-order integrodifferential equations whose order of derivative is one [34], quartic trigonometric B-spline algorithm for numerical solution of the regularized long wave equation [15], an effective application of differential quadrature method based on modified cubic B-splines to numerical solutions of the KdV equation [3], and the exponential cubic b-spline collocation method for the Kuramoto–Sivashinsky equation in [18]
5 Conclusion In our knowledge, so far the exponential spline functions have not been yet applied for approximating the second-order integro-differential equations
Summary
Integro-differential equations have gained a lot of interest in multitude of uses, in sciences related to nature and engineering. Many authors have investigated the numerical methods for integral equations These methods include a cubic spline approximation in C2 to the solution of the Volterra. For second-order impulsive integro-differential equations, periodic boundary value problems are discussed in [47]. 2, non-polynomial spline method to solve second-order boundary value problems of Fredholm integrodifferential equation is described. To develop the consistency relations between the values of spline and its derivatives at knots, consider the following relation: αMi–1 + 2βMi + αMi+1 = h2 (ui+1 – 2ui + ui–1),. Equations (5) and (8) have the following forms: WM = R U, Zm = SU, where W , R, Z, and S are coefficient matrices in (5) and (8). Α and β do not affect the second order of convergence
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