Abbasov, E. M.; Dyshin, O. A.; Suleimanov, B. A. Wavelet method for solving second-order quasilinear parabolic equations with a conservative principal part. (Russian, English) Zbl 1199.65328 Zh. Vychisl. Mat. Mat. Fiz. 49, No. 9, 1629-1642 (2009); translation in Comput. Math., Math. Phys. 49, No. 9, 1554-1566 (2009). Summary: A method based on wavelet transforms is proposed for finding classical solutions to initial-boundary value problems for second-order quasilinear parabolic equations. For smooth data, the convergence of the method is proved and the convergence rate of an approximate weak solution to a classical one is estimated in the space of wavelet coefficients. An approximate weak solution of the problem is found by solving a nonlinear system of equations with the help of gradient-type iterative methods with projection onto a fixed subspace of basis wavelet functions. MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 35K57 Reaction-diffusion equations 65T60 Numerical methods for wavelets 35D30 Weak solutions to PDEs Keywords:weak and approximate weak solutions to initial-boundary value problems for parabolic equations; multiresolution analysis; wavelet basis; gradient-type iterative method; irregular operator equation PDF BibTeX XML Cite \textit{E. M. Abbasov} et al., Zh. Vychisl. Mat. Mat. Fiz. 49, No. 9, 1629--1642 (2009; Zbl 1199.65328); translation in Comput. Math., Math. Phys. 49, No. 9, 1554--1566 (2009) Full Text: DOI Link