The Adomian decomposition method (ADM) was developed in [10] to find an analytical solution to the model in [10]. Recently, in [11], the authors proposed a wavelet technique based on the Chebyshev and Legendre bases to solve the above BVP. A similar method based on the ultra-spherical wavelet was examined in [14]. The optimal homotopy analysis procedure was applied to the model (1) in [15]. The technique of the B-Spline collocation scheme was employed in [16]. A hybrid method based on the modified ADM and quintic B-spline collocation strategy was given in [17]. Moreover, the shifted Chebyshev collocation procedure for the spherical biocatalyst and catalyst models was investigated in [18]. Some other numerical methods developed for the model (1) and the models close to it can be found in [19; 20; 21; 22]. Our purpose here is to propose a new strategy to solve the strongly nonlinear model (1) efficiently and accurately. The present algorithm is based on a combination of the quasilinearization method (QLM) and the spectral collocation approach for the nonlinear model (1). The technique of QLM is first employed to eliminate both the nonlinearity and singularity of the underlying model. The result is a sequence of linearized submodels that have to be solved iteratively. In the second stage, we develop a matrix method based on the (novel) class of polynomials along with certain collocation points to acquire the approximate solutions of this set of linearized equations. This new class of polynomials is very closely related to the Bessel function of Krall and [PERSON]. We further establish the convergence property of these polynomials in the \(L_{2}\) norm. The technique of residual correction is also introduced to improve the accuracy of the already-computed solutions and based on the residual error functions. Over the last decade, thanks to the successful applications of spectral and collocation methods based on (various) polynomial functions, rapid progress has been made towards solving many interesting and challenging model problems in physical and engineering sciences. Among the multitude of used basis functions, we mention the Bessel [23], Laguerre [24], [PERSON] [25; 26], Chebyshev [27], Newton [28], Fibonacci [29], and Morgan-Voyce [30; 31] polynomials. Let us describe the content of this research paper in more detail as follows. A review of main facts associated with this new class of polynomials known as the Chatterjea polynomials (ChPs) is provided in Section 2. In Section 3, we first illustrate the main idea of \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Description** & **Unit** \\ \hline \(\mathbb{S}:\) & Substrate concentration & mol/cm\({}^{3}\) \\ \(M:\) & Dimensionless substrate concentration (\(=\mathbb{S}/\mathbb{S}_{0}\)) & - \\ \(\mathbb{S}_{0}:\) & Bulk-substrate concentration & mol/cm\({}^{3}\) \\ \(D:\) & Effective diffusivity inside the particle & cm\({}^{3}\)/s \\ \(\mathbb{V}_{M}:\) & Maximum reaction rate & mol/s cm\({}^{3}\) \\ \(\mathbb{K}_{M}:\) & Michaelis constant & mol/cm\({}^{3}\) \\ \(k_{m}:\) & External mass-transfer coefficient & mol/cm\({}^{3}\) \\ \(x:\) & Spatial variable & cm \\ \(h:\) & Thiele modulus & - \\ \(\alpha:\) & Dimensionless Michaelis constant & - \\ \(L:\) & Half length of the particle & cm \\ \(s_{h}:\) & Modified Sherwood number & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Nomenclature. QLM. Hence, the hybrid QLM-ChPs algorithm is described in detail. The error bound for the proposed QLM-ChPs scheme is investigated next. The accuracy of the present approach is justified by defining the technique of residual error functions. Finally, in this section, we introduce the technique of residual correction (RC), which helps us to improve the quality of the approximate solutions. We next carry out a set of computational experiments to analyze the computational efficiency as well as the accuracy of the QLM-ChPs procedure for the considered model problem in Section 4. Ultimately, in Section 5, we present the conclusions of the current work.