Two novel Bessel matrix techniques to solve the squeezing flow problem between infinite parallel plates

This study is concerned with the numerical solutions of the squeezing flow problem which corresponds to fourth-order nonlinear equivalent ordinary differential equations with boundary conditions. We have two goals to obtain numerical solutions to the problem in this paper. One of them is to obtain numerical solutions based on the Bessel polynomials of the squeezing flow problem using a collocation method. We call this method the direct method based on the Bessel polynomials. The direct method converts the squeezing flow problem into a system of nonlinear algebraic equations. Next, we aimed to transform the original non-linear problem into a sequence of linear equations with the aid of the technique of quasilinearization then we solve the obtained linear problem by using the Bessel collocation approach. This technique is called the QLM-Bessel method. Both of these techniques produce accurate results when compared to other methods. Error analysis in the weighted $L_2$ and $L_\infty$ norms is presented for the Bessel collocation scheme. Lastly, numerical applications are made on examples and also numerical outcomes are compared with other results available in the literature. It is observe that our results are effective according to other results and also QLM-Bessel method is better than the direct Bessel method.