Caption: Figure 1--Dispersion diagram, simple

non-polynomial regression equation, coefficient of determination ([R.sup.2]) and significance level (P) between levels of fat (A), protein (B), lactose (C) and non-fat solids (D) obtained by ultrasound spectroscopy (EKOMILK total[R], Eon Trading LLC, Bulgaria) and the infrared method-PO ANA 009 (ESALQ/USP).

Keywords: Non-polynomial cubic spline technique, Finite difference approximations, System of partial differential equations, Second order linear Klein-Gordon equation.

The non-polynomial cubic spline method has been used to solve many PDEs (Ramadan et al.

and boundary conditions in equation (3) form a system of PDEs which was solved by using non-polynomial cubic spline method.

In section 3, we investigate two numerical examples of the reaction diffusion equation with polynomial and non-polynomial nonlinearities.

The first five figures (Figures 1 through 5) are related to the numerical results of Example 1, the non-polynomial nonlinearity example.

In Figures 1 and 6, for both non-polynomial and polynomial nonlinearity examples, our perturbation method with two terms P2 is superior to the others for all considered values of [N.sub.p] (10% through 40% of M).

Keywords: Non-polynomial Cubic spline Central finite difference approximations Sixth- order BVPs System of linear algebraic equations.

In this work non-polynomial spline method was used for gaining smooth approximation to the solutions of sixth order BVPs of the form:

This leads to non-polynomial Xu-like inter polation formulas, which work on domains with quite different geometries, like generalized rectangles (in Cartesian coordinates), generalized sectors and starlike domains (in polar coordinates).

Now, by interpolating the composition g = f [omicron] [sigma], at the Xu points in [[-1,1].sup.2], we get a (in general) non-polynomial interpolation formula