Approximate method for solving linear integro-differential equations of order one

In this note, a general form of Fredholm-Volterra integro-differential equation order one is considered. The truncated Legendre series is used as bases function to approximate unknown function and Gauss-Legendre quadrature formula is applied for kernel integrals. Reduced algebraic equations are solved by using collocation method with roots of Legendre polynomials as collocation points. Three numerical examples with the comparisons are provided to show the validity and accuracy of the suggested method. Numerical results reveal that proposed method is dominated with repeated trapezoidal rule and differential transform method. � 2018 Author(s).