This paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. Then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. Finally an example is given to illustrate the performance of the methods.

It is shown how recent ideas on rational Gauss-type quadrature rules can be extended to Gauss-Kronrod, Gauss-Turr an, and Cauchy principal value quadrature rules. Numerical examples illustrate the advantages in accuracy thus achievable. 0. Introduction The idea of constructing quadrature rules that are exact for rational functions with prescribed poles, rather than for polynomials, has received...

We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to L are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule. Key...

Anew approach for creating stable quadrature rules with preassigned points is proposed. The idea is to approximate a known stable quadrature rule by a local interpolation at the preassigned points. The construction cost of the method does not grow as the number of the preassigned points increases. The accuracy of the rule depends only on the accuracy of the chosen stable rule and that of the in...

Quadrature rules estimate ∫ 1 0 f(x) dx when f is defined by a table of n+1 values. Every binary string of length n defines a quadrature rule by choosing which endpoint of each interval represents the interval. The standard rules, such as Simpson’s Rule, correspond to strings of low Kolmogorov complexity, making it possible to define new quadrature rules with no smoothness assumptions, as well ...

We introduce two direct quadrature methods based on linear rational interpolation for solving general Volterra integral equations of the second kind. The first, deduced by a direct application of linear barycentric rational quadrature given in former work, is shown to converge at the same rate as the rational quadrature rule but is costly on long integration intervals. The second, based on a co...

Abstract. Gauss quadrature is a popular approach to approximate the value of a desired integral determined by a measure with support on the real axis. Laurie proposed an (n+1)-point quadrature rule that gives an error of the same magnitude and of opposite sign as the associated n-point Gauss quadrature rule for all polynomials of degree up to 2n + 1. This rule is referred to as an anti-Gauss ru...

In this paper, anti-Gaussian quadrature rules for trigonometric polynomials are introduced. Special attention is paid to an even weight function on [-?, ?). The main properties of such proved and a numerical method their construction presented. That based relations between nodes weights the rule algebraic polynomials. Some examples included. Also, we compare our with other available methods.

The solution of the radiation transfer equation for the Earth's atmosphere needs to account for the re ectivity of the ground. When using the spherical harmonics method, the solution for this term involves an integral with a particular measure that presents numerical challenges. We are interested in computing a high order Gauss quadrature rule for this measure. We show that the two classical al...