A combined approximation method for nonlinear foam drainage equation

The aim of this study is to develop a combined approximative technique to find a numerical solution to the foam drainage equation arising in various absorption and distillation processes. In this approach, first, the discretization of time is performed with the aid of the Taylor expansion series. Hence, a collocation method based on novel Bessel polynomials is utilized for the space variable. Thus the solution is found by solving a linear system of algebraic equations at each time step in contrast to solving a nonlinear system. Numerical simulations are provided to check the accuracy and efficiency of the presented algorithm. The numerical results are compared with exact solutions as well as with the outcomes of other existing available numerical methods.