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This note deals with a new computational method for solving a class of singular boundary value problems. The method is based upon Bernstein Polynomials. The properties of Bernstein Polynomials, together with Bernstein operational matrix for differentiation formula, are presented and utilized to reduce the given singular boundary value problems to the set of algebraic equations. The proposed method is applied to solve some test problems with the comparison between the computational solutions and the exact solutions. The results indicate that the proposed algorithm provides high reliability and good accuracy.

An efficient numerical method is presented for solving the initial value problems of Bratu-type equations using Chebyshev wavelets. To the best of our knowledge, until now there is no rigorous Chebyshev wavelet solutions have been reported for the initial value problems of Bratu-type equations. The scheme is based on a novel operational matrix derived from integration of Chebyshev wavelets. Some examples are included to demonstrate the validity and applicability of the technique. The calculated results as compared with those calculated by other methods, illuminate the efficiency and precision of Chebyshev Wavelet Method (CWM) for this problem. The power of the manageable method is confirmed. The results show that the proposed way is quite reasonable when compared to exact solution and other classical methods.

In this paper, we have established an efficient wavelet based approximation method to solve film-pore diffusion model (FPDM) arising in engineering. Film pore diffusion model is widely used to determine study the kinetics of adsorption systems. The use of wavelet based approximation method is found to be accurate, simple, fast, flexible, convenient, and computationally attractive. The present paper focus that FPDM satisfactorily describes the kinetics of methylene blue adsorption onto the three low-cost adsorbents, guava, teak, and gulmohar plant leaf powders used in this study.

In this paper, a wavelet based hybrid method is employed to provide the quick and accurate solutions of fractional Black-Scholes equation with boundary condition for a European option pricing (EOP) problem. The fractional Black-Scholes is used as a model for valuing European or American call and put options on a non-dividend paying stock. To the best of our knowledge, until now there is no rigorous Legendre wavelet solutions have been reported for the fractional Black-Scholes