Computational study of non-linear integer and time-fractional foam drainage equations using radial basis functions

Abstract

In this article, radial basis function (RBFs) based method is suggested to study non-linear Foam Drainage and Fractional Foam Drainage Equations. For this purpose, θ-weighted scheme is implemented along with the quasi-linearization technique on the spatial part to linearize the non-linear terms. Finite difference along with Crank–Nicholson is used for time discretization. Numerical results are computed to validate the technique’s accuracy while solving the fractional and classical foam drainage equations. A comparative analysis with other methods proved it to be one of the efficient and practical approaches. An algorithm is applied to get the optimal value of the involved shape parameter “c” to get better accuracy. Stability analysis is done to check how far the model remains stable. The efficiency and accuracy of the proposed scheme are further examined via mass and energy conservation laws.

Keywords

• RBF approximation
• Foam drainage equation
• Fractional foam drainage equation
• Non linear PDEs
• Shape parameter
• Stability