Further Study On B-Spline Quasi-Interpolants

The B-spline quasi-interpolant has some good properties,for example,it is local,easy to calculate and very efficient.Compared with interpolation method and least square method,quasi-interpolant method does not need to solve any linear equations.Therefore,when the spatial dimension of the problem is larger,the advantage of quasi-interpolat is more distinct.The B-spline quasi-interpolant has a wide range of applications in mechanics,mathematical statistics,electricity and scientific calculation.In this paper,a further study is carried out.A.Boujraf et al,in 2015,studied the spline quasi-interpolant which is based on functional integral values,it is frequently used in climatology,engineering,environmental science and oceanography.C.Allouch et al proposed the superconvergent spline quasi-interpolants in 2017.The quasi-interpolant of degree d has optimal convergence order(?^?9+1?,and there is superconvergence phenomenon at the nodes.In this paper,a new cubic B-spline quasi-interpolant is proposed on the basis of the above two quasi-interpolants.The quasi-interpolant constructed by us has higher approximation accuracy.In addition,a high-order accuracy numerical differential formula is also given in this paper.Finally,numerical results are given to illustrate the theoretical ones.