B. V. Rathish Kumar

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In this study we propose a space and time-accurate numerical method for Korteweg– de Vries equation. In deriving the computational scheme, Taylor generalized Euler time discretization is performed prior to wavelet based Galerkin spatial approximation. This leads to the implicit system which can also be solved by explicit algorithms. Korteweg– de Vries(More)
SUMMARY In this paper we propose a wavelet Taylor–Galerkin method for the numerical solution of time-dependent advection–diiusion problems. The discretization in time is performed before the spatial discretization by introducing second-and third-order accurate generalization of the standard time stepping schemes with the help of Taylor series expansions in(More)
In this study wavelet based high-order Taylor Galerkin methods is introduced. Additional time layers are used to obtain high-order temporal accuracy unattainable within a two-step strategy. Two explicit model schemes are constructed and asymptotic stability of schemes are verified. The compactly supported orthogonal wavelet bases developed by Daubechies are(More)
In this paper, we propose a wavelet-Taylor–Galerkin method for solving the two-dimensional Navier–Stokes equations. The discretization in time is performed before the spatial discretization by introducing second-order generalization of the standard time stepping schemes with the help of Taylor series expansion in time step. Wavelet-Taylor–Galerkin schemes(More)
We introduce the concept of fast wavelet-Taylor Galerkin methods for the numerical solution of partial differential equations. In wavelet-Taylor Galerkin method discretization in time is performed before the wavelet based spatial approximation by introducing accurate generalizations of the standard Euler, ␪ and leapfrog time-stepping scheme with the help of(More)
In this study, we derive error estimates for time accurate wavelet based schemes in two stages. First we look at the semi-discrete boundary value problem as a Cauchy problem and use spectral decomposition of self adjoint operators to arrive at the temporal error estimates both in L 2 and energy norms. Later, following the wavelet approximation theory, we(More)
A class of efficient preconditioners based on Daubechies family of wavelets for sparse, unsymmetric linear systems that arise in numerical solution of Partial Differential Equations (PDEs) in a wide variety of scientific and engineering disciplines are introduced. Complete and Incomplete Discrete Wavelet Transforms in conjunction with row and column(More)