Technique for solving minimum of integral function by Legendre wavelet

Volume 1, Issue 1, October 2016     |     PP. 44-52      |     PDF (213 K)    |     Pub. Date: October 17, 2016
DOI:    2471 Downloads     19175 Views  

Author(s)

Xiaoyang Zheng, College of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, China
Hong Su, College of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, China
Liqiong Qiu, College of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, China
Jiangping He, College of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, China

Abstract
This presents a refined approach for computing integral and product operators by using the rich properties of Legendre wavelet.The most advantages of this refined calculations are that the operational matrices are lower dimensions, coarse and its elements are the same on each subinterval, respectively. The operational matrices are applied to solving the minimum of integral function from heat conduction problem. The essence of this technique is to transform the optimization of integral function into that of Legendre wavelet coefficients, which is solved by Lagrange-multiplier method. The good results demonstrate that this technique is valid and applicable.

Keywords
Legendre wavelet; operational matrix of integration; operational matrix of product; refined calculation; minimum of integral function.

Cite this paper
Xiaoyang Zheng, Hong Su, Liqiong Qiu, Jiangping He, Technique for solving minimum of integral function by Legendre wavelet , SCIREA Journal of Mathematics. Volume 1, Issue 1, October 2016 | PP. 44-52.

References

[ 1 ] R.S. Schechter, The Variation Method in Engineering, McGraw-Hill, New York, 1967.
[ 2 ] C.F. Chen, C.H. Hsiao, A Walsh series direct method for solving variational problems, J. Franklin Inst. 300 (1975) 265–280.
[ 3 ] F. Khellat and S.A. Yousefi, The linear Legendre mother wavelets operational matrix of integration and its application, Journal of the Franklin Institute, 343 (2006) 181-190.
[ 4 ] Yousefi, S.: Legendre wavelets method for solving differential equations of Lane-Emden type, Appl. Math. Comput. 181, 1417--1422 (2006)
[ 5 ] B.Alpert, G.Beylkin, D.Gines and L.Vozovoi, Adaptive solution partial differential equations in multiwavelet bases, J. Comput. Phys. 182 (2002) 149–190.
[ 6 ] B.Alpert, A Class of Bases in L2 for the Sparse Representation of Integral Operators, SIAM J.Math.Anal. 24 (1993) 247–262.
[ 7 ] G.Beylkin, On the representation of operators in bases of compactly supported wavelets, SIAM. J. Numer. Anal. 6 (1992) 1716–1739.
[ 8 ] M.Razzaghi and S.Yousefi, Legendre wavelets direct method for variational problems, Math.Comput.Simulation. 53 (2000) 190–190.
[ 9 ] K.Maleknejad, N.Aghazadeh and F.Molapourasl, Numerical solution of Fredholm integral equation of the first kind with collocation method and estimation of error bound, Appl.Math.Comput. 179 (2006) 352–359.