An efficient wavelet based spectral method to singular boundary value problems

Abstract

In this paper, we have established an efficient wavelet based approximation method to nonlinear singular boundary value problems. To the best of our knowledge, until now there is no rigorous shifted second kind Chebyshev wavelet (S2KCWM) solution has been addressed for the nonlinear differential equations in population biology. With the help of shifted second kind Chebyshev wavelets operational matrices, the nonlinear differential equations are converted into a system of algebraic equations. The convergence of the proposed method is established. The power of the manageable method is confirmed. Finally, we have given some numerical examples to demonstrate the validity and applicability of the proposed wavelet method.

A reduced computational matrix approach with convergence estimation forsolving model differential equations involving specific nonlinearities ofquartic type

“…The above equation constrained by the boundary conditions can be solved via the proposed method. In Table 4, we compare the numerical results of the Mott polynomial solutions with the existing ones, which were previously obtained by the shifted second-kind Chebyshev wavelet method (CWM) [26], the Adomian decomposition method with Green functions [28], and the variational iteration method (VIM) [15]. It is easy to see that the present results are in good agreement with the others.…”

“…Model 6.6. [2,7,15,26,28] Consider the singular nonlinear differential equation modeling the radial stress on a rotationally symmetric shallow membrane cap:…”

“…Bülbül and Sezer [4,5] established the Taylor polynomial method to find the approximate solutions of nonlinear differential equations of Abel and Duffing types. Rajaraman and Hariharan [26] proposed the shifted second-kind Chebyshev wavelet method to solve singular boundary value problems. The Green function-based Adomian decomposition method and variational iteration method have been used for singular nonlinear boundary value problems [15,28].…”

“…Comparison of the numerical results of the solutions for Model 6.6. t i y 5 (t i ; 0.6) CWM[26] GFADM[28] VIM[15] …”

An efficient Chebyshev wavelet based analytical algorithm to steady state reaction–diffusion models arising in mathematical chemistry

“…The wavelet based approximation methods had been compared with Adomian decomposition method and other classiclal Recently, Rajaraman and Hariharan [13,14] had introduced the efficient wavelet based spectral methods to singular boundary value problems and nonlinear reaction-diffusion problems. Hariharan and his coworkers [15][16][17] had developed the wavelet based approximation methods to differential equations.…”