A pseudo-spectral method based on reproducing kernel for solving the time-fractional diffusion-wave equation

In this paper, we focus on the development and study of the finite difference/pseudo-spectral method to obtain an approximate solution for the time-fractional diffusion-wave equation in a reproducing kernel Hilbert space. Moreover, we make use of the theory of reproducing kernels to establish certain reproducing kernel functions in the aforementioned reproducing kernel Hilbert space. Furthermore, we give an approximation to the time-fractional derivative term by applying the finite difference scheme by our proposed method. Over and above, we present an appropriate technique to derive the numerical solution of the given equation by utilizing a pseudo-spectral method based on the reproducing kernel. Then, we provide two numerical examples to support the accuracy and efficiency of our proposed method. Finally, we apply numerical experiments to calculate the quality of our approximation by employing discrete error norms. © 2022, The Author(s)

Low temperature dye-sensitized solar cells based on conformal thin zinc oxide overlayer on mesoporous insulating template by atomic layer deposition

Low temperature processing of dye-sensitized solar cells (DSCs) is essential to enable commercialization with low cost plastic substrates and diminish the overall manufacturing cost.We report a low temperature processing route for photoanodes where thin ZnO nanoshell is deposited by atomic layer deposition at 150°C, on a mesoporous insulating template. We found that a 6 nm ZnO overlayer on a 3 μm mesoporous nanoparticle Al2O3 template shows a power conversion efficiency of 4.2 % with the standard organic sensitizer (coded Y123) and cobalt bipyridine redox mediator