Geodesic
Wavelet method for solving second-order quasilinear parabolic equations with a conservative principal part
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1629-1642

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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. 
@article{ZVMMF_2009_49_9_a9,
     author = {E. M. Abbasov and O. A. Dyshin and B. A. Suleimanov},
     title = {Wavelet method for solving second-order quasilinear parabolic equations with a~conservative principal part},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1629--1642},
     publisher = {mathdoc},
     volume = {49},
     number = {9},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a9/}
}
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E. M. Abbasov; O. A. Dyshin; B. A. Suleimanov. Wavelet method for solving second-order quasilinear parabolic equations with a conservative principal part. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1629-1642. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a9/