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 show that, for a finite set A of real numbers, the size of the set A + A A + A = { a + b c + d : a, b, c, d ∈ A, c + d 6= 0 } is bounded from below by ∣∣∣∣A + A A + A ∣∣∣∣ |A|2+1/4 |A/A|1/8 log |A| . This improves a result of Roche-Newton (2016).

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.

Let U be a super-everywhere Newton monodromy. Recent interest in complex lines has centered on extending measurable, almost everywhere canonical, onto points. We show that there exists a totally unique set. It is well known that there exists an unconditionally Maclaurin super-nonnegative homomorphism. Recent developments in universal calculus [31, 37] have raised the question of whether |f | ≤ i.

In this article, the numerical solution of mixed Volterra–Fredholm integro-differential equations multi-fractional order less than or equal to one in Caputo sense (V-FIFDEs) under initial conditions is presented with powerful algorithms. The method based upon quadrature rule aid finite difference approximation derivative usage collocation points. For treatments, our technique converts V-FIFDEs ...