In this paper, a reproducing kernel with polynomial form is used for finding analytical and approximate solutions of a second-order hyperbolic equation with linear initial-boundary conditions. The analytical solution is represented as a series in the reproducing kernel space, and the approximate solution is obtained as an n-term summation. Error estimates are proved to converge to zero in the s...

Perez, F.F. and Fraga, F., 1987. A precise and rapid analytical procedure for alkalinity determination. Mar. Chem., 21: 169-182. A potentiometric analytical method is proposed for the determination of the alkalinity of seawater. The precision is 0.1% and each determination takes 3 min. The technique is very easy to use, even on board ship since it is carried out in open flasks. A polynomial equ...

Abstract: In this paper, we apply the shifted Legendre polynomial method (SLPM) to solve the fractional Volterra’s model for population growth of a species in a closed system. The SLPM solution procedure for nonlinear fractional integro-differential equations is established. Moreover, the accurate analytical approximations are obtained, which are valid and convergent for different fractional or...

A new method Is presented for determining the moments of nuclear magnetic resonance absorption lines from the shape of either the free Induction decay or that of the echo. Unlike previously used techniques, this method does not require the assumption of an analytical function for the lineshape or the fitting of the experimental decay with a polynomial. A fast, suitably precise and numerically s...

Fractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. Analytical solution of many applications, where the fractional differential equations appear, cannot be established. Therefore, cubic polynomial splinefunction-based method combined with shooting method is considered to find approximate solution for a class of fract...