Abstract
AbstractIn this paper, a kind of bivariate Bernoulli-type multiquadric quasi-interpolation operator is studied by combining the known multiquadric quasi-interpolation operator with the generalized Taylor polynomial as the expansion in the bivariate Bernoulli polynomials. Some error bounds and convergence rates of the combined operators are studied. A selection of numerical examples is presented to compare the performances of the obtained scheme. Furthermore, our method can be applied to time-dependent differential equations. Its advantage is that the algorithm is very simple and easy to implement.
Funder
the Science and Technology Research Projects of the Education Office of Jilin Province
the Open Project of Key Laboratory of Symbolic Computing and Knowledge Engineering of Ministry of Educatio
the School Level Projection of Jilin University of Finance and Economics
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference42 articles.
1. Rabut, C.: An introduction to Schoenberg’s approximation. Comput. Math. Appl. 24, 149–175 (1992)
2. De Boor, C., Ron, A.: Fourier analysis of the approximation power of principal shift-invariant spaces. Constr. Approx. 8, 427–462 (1992)
3. Bozzini, M., Dyn, N., Rossini, M.: Construction of generators quasi-interpolation operators of high approximation orders in spaces of polyharmonic splines. J. Comput. Appl. Math. 236, 557–564 (2011)
4. Strang, G., Fix, G.: A Fourier analysis of the finite-element variational method. In: Geymonat, G. (ed.) Constructive Aspects of Functional Analysis, pp. 793–840. C.I.M.E., Rome (1993)
5. Jia, R.Q.: A new version of the strang-fix conditions. J. Approx. Theory 74, 221–225 (1993)
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献