APPROXIMATION OF A FUNCTION HAVING BOUNDED DERIVATIVES UPTO THE SECOND ORDER BY SINE-COSINE WAVELET EXPANSION AND ITS APPLICATIONS
Copyright policy )APPROXIMATION OF A FUNCTION HAVING BOUNDED DERIVATIVES UPTO THE SECOND ORDER BY SINE-COSINE WAVELET EXPANSION AND ITS APPLICATIONS
Summary: In this paper, sine-cosine wavelet has been introduced and the approximation errors of the function \(f(t)\) whose first and second derivatives are bounded have been estimated using this wavelet and it is used to solve some linear differential equations. Solution obtained by this method is compared with Euler's method and with exact solution. We observe that the solution obtained by this method is better than the solution given by the Euler's method which shows the usefulness of this method.
Numerical solution of boundary value problems involving ordinary differential equations, orthonormal set, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, Numerical methods for wavelets, Nontrigonometric harmonic analysis involving wavelets and other special systems, General harmonic expansions, frames, sine-cosine wavelet, wavelet approximation, operational matrix of integration, Numerical methods for integral equations
Numerical solution of boundary value problems involving ordinary differential equations, orthonormal set, Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations, Numerical methods for wavelets, Nontrigonometric harmonic analysis involving wavelets and other special systems, General harmonic expansions, frames, sine-cosine wavelet, wavelet approximation, operational matrix of integration, Numerical methods for integral equations
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