American Journal of Computational Mathematics

Volume 1, Issue 3 (September 2011)

ISSN Print: 2161-1203   ISSN Online: 2161-1211

Google-based Impact Factor: 0.42  Citations  

Haar Wavelet Quasilinearization Approach for Solving Nonlinear Boundary Value Problems

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DOI: 10.4236/ajcm.2011.13020    6,598 Downloads   14,703 Views  Citations

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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.

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H. Kaur, R. Mittal and V. Mishra, "Haar Wavelet Quasilinearization Approach for Solving Nonlinear Boundary Value Problems," American Journal of Computational Mathematics, Vol. 1 No. 3, 2011, pp. 176-182. doi: 10.4236/ajcm.2011.13020.

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