The object of this paper is to obtain the existence, uniqueness and upper bounds for errors of six degree spline interpolating the lacunary data (0,2,5). We also showed that the changes of the boundary conditions and the class of spline functions has a main role in minimizing the upper bounds for error in lacunary interpolation problem. For this reason, in the construction of our spline function which interpolates the lacunary data (0,2,5), we changed the boundary conditions and the class of spline functions which are given by (1) from first derivative to third derivative and the class of spline function from ) 1 , 0 ( 2 C to )

/pdf/the-existence-uniqueness-and-upper-bounds-for-errors-of-six-5u8w7cr5xu.pdf

The Existence, Uniqueness And Upper Bounds For Errors Of Six Degree Spline Interpolating The Lacunary Data (0,2,5)

This paper surveys and reviews paper of spline degree seven inhomogeneous and optimized the best errors bound by spline (0,2, 5; 0, 3, 6) case. It has been shown that the existence, uniqueness and convergence analysis with minimizing the error bounds of deficient seventh spline interpolated.

/pdf/inhomogeneous-lacunary-interpolation-and-optimization-errors-1mjmoarx9e.pdf

Inhomogeneous Lacunary Interpolation and Optimization Errors Bound of Seventh Spline

For solving differential equations, a variety of numerical methods are available, accuracy, performance, and application are all different. In this article, we proposed new numerical techniques for solving the generalized regularized long wave equation(GRLWE) that are based on types M and M-1 of B-splines-least-square method (BSLSM) and weight function of B-splines respectively, which were proposed previously for solving integro-differential equations [2] where $Min {N}$.  We investigated linear stability using a Fourier method.

https://ijnaa.semnan.ac.ir/article_5468_89f38ae584cf4dd9e99c8b5ddc7c6f92.pdf

Combining B-spline least-square schemes with different weight functions to solve the generalized regularized long wave equation

A solid-state lubricant powders is one of the most significant powders usedto protect surfaces from damage in cases of relative motion, with a reduction in thefriction and wear between them. In this study, molybdenum disulfide (MoS2),purity 99%, nanoparticles have been used as solid-state lubrication, due to it havinga low coefficient of friction and high wear resistance. In which MoS2 particles havebeen distributed with 1.69 x 1015 particles per m2 over the steel disc’s surfaceagainst the steel pin using a pin on disc tribometer machine. The pin on disctechnique was used to study the friction coefficient behaviour of the MoS2distribution particles and the position depth of the steel pin on the steel disc surfacewhen the ambient environment was air and humidity. It was used to examine thetribological behaviour of the steel pin on the steel disc surface with no distributionof MoS2 nanoparticles and also for a steel pin on steel disc with a distribution ofMoS2 nanoparticles. Then, the morphologies and microstructures of thedistributions of MoS2 nanoparticles were characterized using Scanning ElectronMicroscopy (SEM). In a result, the distribution of MoS2 nanoparticles have resultedin a lower friction coefficient and higher wear resistance compared with only steelpin on steel disc surfaces.

http://jgu.garmian.edu.krd/article_65662_525057ffa4be40dff1035dfbde54a02b.pdf

Generalization of (0,2,5)Lacunary interpolation by sixtic splines on uniform meshes

/pdf/lacunary-interpolation-using-quartic-b-splin-22pfjwna2v.pdf

Lacunary Interpolation Using Quartic B-Splin

We changed the boundary conditions and the class of spline functions from first derivative to fourth derivative. It was observed that and we show that the change of the boundary conditions and the class of spline functions affect in minimizing the error bounds for lacunary interpolation by spline function. Key words: Spline function INTRODUCTION During the late middle of twentieth century theory of splines has received considerable .According to Schoenberg [9] ,the interest in spline functions is due to the fact that ,spline functions are a good tool for the numerical approximation of functions on the one hand and that they suggest new, challenging and rewarding problems on the other. Piecewise linear functions, as well as step functions ,have long been an important theoretical and practical tools for approximation of functions. A notable exception was the work done by actuarial mathematicians on the so called 'osulatory interpolation 'that began soon after Hermite's work on interpolation. For more information about a spline function ,one is referred to Alberg, Nilson and Walsh

K. H. Jwamer

Papers

Minimizing Error Bounds in (0,2,3) Lacunary Interpolation by Sextic Spline Function