An Efficient Operational Matrix Method for a Few Nonlinear Differential Equations Using Wavelets

In this paper, a theoretical model of biofiltration of mixture of hydrophilic (methanol) and hydrophobic (α-pinene) volatile organic compounds is discussed. An efficient wavelet-based operational matrix method is developed for the analytical expressions pertaining to the concentration profiles of methanol and α-pinene in the air stream and bio-film stream. The convergence and supporting analysis of the proposed method is discussed. The operational matrix of derivatives contains many zero entries, which lead to the high efficiency of the method and reasonable accuracy is achieved even with less number of collocation points. Our results are in good agreement with the Bernstein polynomial method and Adomian decomposition method. The efficiency of the proposed method is confirmed by using computational CPU runtime.