An algorithm for solving linear Volterra integro-differential equations

Exponential spline for the numerical solutions of linear Fredholm integro-differential equations

“…Recently, many authors have investigated the numerical methods for integral equations. These methods include a cubic spline approximation in C 2 to the solution of the Volterra integral equation of the second kind [33], quintic B-spline method [30], Bernstein operational matrix of derivative [4], hybrid of block pulse functions and normalized Bernstein polynomials [5], iterative method [49], sinc-collocation method [48], bivariate splines on nonuniform partitions [36], Jacobi operational matrices for solving delay or advanced integro-differential equations [40], the tau approximation for the Volterra-Hammerstein integral equations [21], b-spline collocation and cubature formulas [12] and [37], wavelet method [6], Walsh function method [35], Chebyshev finite difference method [13], differential transform method [7], Legendre polynomial method [39], an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type [20], CAS wavelets method [22], an efficient matrix method based on Bell polynomials for solving nonlinear Fredholm-Volterra integral equations [32], collocation methods [10], Taylor polynomial methods [46], and Bernoulli matrix method [9]. Xuhao Li and Patricia J.Y.…”