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G. Vainikko, A. Kivinukk and J. Lippus, “Fast Solvers of Integral Equations of the Second Kind: Wavelet Methods,” Journal of Complexity, Vol. 21, No. 2, 2005, pp. 243-273. doi:10.1016/j.jco.2004.07.002

has been cited by the following article:

• TITLE: Haar Wavelet Quasilinearization Approach for Solving Nonlinear Boundary Value Problems

  AUTHORS: Harpreet Kaur, R.C. Mittal, Vinod Mishra

  KEYWORDS: Haar Wavelets, Quasilinearization Technique, Haar Collocation Method, Boundary Value Problems

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.1 No.3, September 19, 2011

  ABSTRACT: Objective of our paper is to present the Haar wavelet based solutions of boundary value problems by Haar collocation method and utilizing Quasilinearization technique to resolve quadratic nonlinearity in y. More accurate solutions are obtained by wavelet decomposition in the form of a multiresolution analysis of the function which represents solution of boundary value problems. Through this analysis, solutions are found on the coarse grid points and refined towards higher accuracy by increasing the level of the Haar wavelets. A distinctive feature of the proposed method is its simplicity and applicability for a variety of boundary conditions. Numerical tests are performed to check the applicability and efficiency. C++ program is developed to find the wavelet solution.