The use of computer algebra systems in a course on scientific computation is demonstrated. Various examples, such as the derivation of Newton’s iteration formula, the secant method, Newton–Cotes and Gaussian integration formulas, as well as Runge–Kutta formulas, are presented. For the derivations, the computer algebra system Maple is used.

In this paper a higher-order numerical solution of a non-linear Volterra integro-differential equation is discussed. Example of this question has been solved numerically using the Runge-Kutta-Verner method for Ordinary Differential Equation (ODE) part and Newton-Cotes formulas for integral parts.

In this paper, we found the error bounds for one of open Newton–Cotes formulas, namely Milne’s formula differentiable convex functions in framework fractional and classical calculus. We also give some mathematical examples to show that newly established are valid formula.

This work is devoted to the study of integration with respect to binomial measures. We develop interpolation quadrature rules and study their properties. Applying a local error estimate based on null rules, we test two automatic integrators with local quadrature rules that generalize the five points Newton Cotes formula.

A function and its first two derivatives are estimated by convolutions with well-chosen non-differentiable kernels. The convolutions are in turn approximated by Newton–Cotes integration techniques with the aid of a polynomial interpolation based on an arbitrary finite set of points. Precise numerical results are obtained with far fewer points than that in classic SPH, and error bounds are deriv...

In this paper, we use parametric form of fuzzy number, then feed-forward neural network is presented for obtaining approximate solution for fuzzy Fredholm integro-differential equation of the second kind. This paper presents a method based on neural networks and Newton-Cotes methods with positive coefficient. The ability of neural networks in function approximation is our main objective. The pr...

We discuss a recursive family of iterative methods for the numerical approximation of roots of nonlinear functions in one variable. These methods are based on Newton-Cotes closed quadrature rules. We prove that when a quadrature rule with n+ 1 nodes is used the resulting iterative method has convergence order at least n+ 2, starting with the case n = 0 (which corresponds to the Newton’s method).