A Review on the Efficiency of Iterative Techniques for Solving Multivariate Nonlinear Particulate Problems

ABSTRACT The multivariate modeling of aggregation and collisional breakage phenomena together with particle growth and source, including spatial diffusion, is considered in this article. These models largely remain unexplored due to the nonlinearity and nonlocal nature of the model equation. The discretization‐based sectional methods lead to a highly complicated grid‐dependent mathematical formulation, which makes it computationally expensive and also affects the stability of the discrete scheme. It is also very tedious to extend such schemes for multivariate models. To address these challenges, we propose and design a semi‐analytical meshfree homotopy‐based solution strategy. To assess the accuracy and efficiency of the proposed technique, we also design two semi‐analytical approaches, namely, the Temimi–Ansari method and the Daftardar–Jafari method for solving the considered model. Efficiency of the homotopy‐based method is assessed with respect to the accuracy toward the prediction of solution and significant moment functions. Numerical examples with physics‐embedded Brownian motion kernel, having applications in linear polymer behavior, are solved to assess the accuracy and efficiency of the new strategy. The results show that the homotopy‐based method is more robust and versatile compared to the other two methods.