Study On Approximation Performance Of MQ Radial Basis Function And Numerical Solution Of Nonlinear Integral Equation

Interpolation is a classical and important method of function approximation.With the development of radial basis function,more and more researchers have constructed interpolation function based on this,and got better results.However,when the interpolation nodes are too many,the ill condition of the interpolation matrix will be caused,and the results obtained by numerical experiments are not ideal.In order to overcome this problem,a new quasi interpolation scheme is constructed based on WuSchabak quasi interpolation scheme and five point differential formula.It has the advantages of polynomial reproducibility,conformability and high convergence order.The numerical experiments show that the proposed quasi interpolation scheme has a good approximation accuracy after selecting the appropriate shape parameters.The main work of this paper is briefly described below.(1)A new radial quasi interpolation operator is constructed based on Wu Schaback’s Quasi interpolation operator and five point numerical differential formula.Through theoretical analysis,the linear polynomial reproducibility,second-order shape preserving and convergence of the operator are discussed in detail,and the convergence order of the numerical scheme is improved.Finally,in the numerical experiment,the approximation ability of the quasi interpolation operator is compared with Wu-Schaback’s Quasi interpolation scheme and Feng Li’s Quasi interpolation scheme.The numerical experiment results verify the correctness of the theory and show the effectiveness of the operator.(2)Based on the second kind of nonlinear Volterra integral equation,this paper combines the Bessel polynomial series with collocation method,and successfully transforms the equation system into a system of linear equations with Bessel coefficients.Its numerical structure is relatively stable.The convergence and error analysis of this method are given,and the higher order of convergence is achieved.Through the comparison of numerical experimental results,the positive effect of the theory is verified the accuracy and the superiority of the numerical algorithm.