Abstract
where \(\varGamma ,\varLambda \) are given constants and \(D_\gamma {}_\lambda \), f are prescribed functions.
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References
Abe, K., Koro, K., Itami, K.: An h-hierarchical Galerkin BEM using Haar wavelets. Eng. Anal. Bound. Elem. 25, 581–591 (2001)
Aziz, I., Siraj-ul-Islam, Sarler, B.: Wavelets collocation methods for the numerical solution of elliptic BV problems. Aplied. Math. Model. 37, 676–694 (2013)
Bujurke, N., Salimath, C., Kudenatti, R., Shiralashetti, S.: A fast wavelet-multigrid method to solve elliptic partial differential equations. Appl. Math. Comput. 185, 667–680 (2007)
Çelik, I.: Haar wavelet approximation for magnetohydrodynamic flow equations. Appl. Math. Model. 37, 3894–3902 (2013)
Chen, X., Xiang, J., Li, B., He, Z.: A study of multiscale wavelet-based elements for adaptive finite element analysis. Adv. Eng. Softw. 41, 196–205 (2010)
Christon, M.A., Roach, D.W.: The numerical performance of wavelets for PDEs: the multi-scale finite element. Comput. Mech. 25, 230–244 (2000)
Dahmen, W., Kurdila, A., Oswald, P.: Multiscale wavelet methods for partial differential equations. Academic Press, New York (1997)
Gaur, S., Singh, L., Singh, V., Singh, P.: Wavelet based multiscale scheme for two-dimensional advection-dispersion equation. Appl. Math. Model. 37, 4023–4034 (2013)
Koro, K., Abe, K.: Application of Haar wavelets to time-domain BEM for the transient scalar wave equation. IOP Conf. Ser.: Mater. Sci. Eng. 10 (2010). doi:10.1088/1757-899X/10/1/012222.
Lepik, Ü.: Solving PDEs with the aid of two-dimensional Haar wavelets. Comput. Math. Appl. 61, 1873–1879 (2011)
Mai-Duy, N., Tanner, R.: A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems. J. Comput. Appl. Math. 201, 30–47 (2007)
Salazar, A., Lorduy, G.H.: Approach to wavelet multiresolution analysis using Coiflets and a two-wave mixing arrangement. Optics Commun. 281, 3091–3098 (2008)
Schwab, C., Stevenson, R.: Adaptive wavelet algorithms for elliptic PDEs on product domains. Math. Comput. 77, 71–92 (2008)
Shi, Z., Cao, Y., Chen, Q.: Solving 2D and 3D Poisson equations and biharmonic equations by the Haar wavelet method. Appl. Math. Model. 36, 5143–5161 (2012)
Siraj-ul-Islam, Sarler, B., Aziz, I., Fazal-i-Haq: Haar wavelet collocation method for the numerical solution of boundary layer fluid flow problems. Int. J. Thermal Sci. 50, 686–697 (2011)
Wang, M., Zhao, F.: Haar wavelet method for solving two-dimensional Burgers equation. Adv. Intell. Soft Comput. 145, 381–387 (2012)
Zheng, X., Yang, X., Su, H., Qiu, L.: Discontinuous Legendre wavelet element method for elliptic partial differential equations. Appl. Math. Comput. 218, 3002–3018 (2011)
Zhou, X., He, Y.: Using divergence free wavelets for the numerical solution of the 2-D stationary Navier-Stokes equations. Appl. Math. Comput. 163, 593–607 (2005)
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Lepik, Ü., Hein, H. (2014). Solving PDEs with the Aid of Two-Dimensional Haar Wavelets. In: Haar Wavelets. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-04295-4_7
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