This work presents different numerical methods that are used for the first time in solving Perovskite solar cells (PSCs). Classical differential quadrature, sinc, and discrete singular convolution (Regularized Shannon and Delta Lagrange kernels) methods are employed for studying this problem. The governing equations are derived based on Poisson's and continuity equations. The different quadrature techniques are introduced to convert the system of nonlinear partial differential equations to nonlinear algebraic system. Then, an iterative method is used to solve this system. Convergence and efficiency of the obtained results with error ≤10
8 depend on various computational characteristics for each technique. The computed results match with previous experiment, exact, finite difference, SCAPS 1-D simulation software, and finite element scheme. Then, the comprehensive parametric study is explored to show the effects of density states, gap energy, thickness, temperatures, lifetimes, wavelength, absorption coefficient, recombination prefactor, and recombination mechanisms whether direct or indirect on power conversion efficiency (PCE) and charge transport of solar cells with and without interface material. After all that have been studied on PSCs, it was found that the best value of PCEs was 32%. Thus, the computed results of the present schemes may be useful for improving the performance level of PSCs.