It is proved that a discrete delta function introduced by P. Smereka [10] gives a second-order accurate quadrature rule for surface integrals using values on a regular background grid. The delta function is found using a technique of A. Mayo [7]. It can be expressed naturally using a level set function.

We present an overview of approaches to selfvalidating one-dimensional integration quadrature formulas and a verified numerical integration algorithm with an adaptive strategy. The new interval integration adaptive algorithm delivers a desired integral enclosure with an error bounded by a specified error bound. The adaptive technique is usually much more efficient than Simpson’s rule and narrow...

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations...

After some remarks on the convergence order of the classical gaussian formula for the numerical evaluation of integrals on unbounded interval, the authors develop a new quadrature rule for the approximation of such integrals of interest in the practical applications. The convergence of the proposed algorithm is considered and some numerical examples are given.

In this paper, we suggest and analyze a new two-step iterative method for solving nonlinear fuzzy equations using the Midpoint quadrature rule. The fuzzy quantities are presented in parametric form. Sever examples are given to illustrate the efficiency of the proposed method. Mathematics Subject Classification: 03E72; 37C25

A numerical method for solving nonlinear Fredholm-Volterra integral equations is presented. The method is based upon Lagrange functions approximations. These functions together with the Gaussian quadrature rule are then utilized to reduce the Fredholm-Volterra integral equations to the solution of algebraic equations. Some examples are included to demonstrate the validity and applicability of t...

Stability limits for the diagonal forms approximating the free space Green’s function in Helmholtz’ equation are derived. It is shown that while the original approximation of the Green’s function is stable except for overflows, the diagonalized form becomes unstable due to errors from roundoff, interpolation, choice of quadrature rule and approximation of the translation operator. Numerical exp...

In this paper we analyse the iterated discrete Legendre Galerkin method for Fredholm-Hammerstein integral equation with a smooth kernel. Using a sufficiently accurate numerical quadrature rule, we obtain super-convergence rates for the iterated discrete Legendre Galerkin solutions in both infinity and L-norm. Numerical examples are given to illustrate the theoretical results.