Amit Prakash

In this article, we employ a hybrid methodology, ISTT by combining the “Sumudu transform” and the “Gejji–Jafari iterative technique” to obtain an approximate series solution of the fractional nonlinear Keller–Segel equation. The method is applied to three examples with different sensitivity functions and the obtained solutions are presented through graphical visualizations. The obtained results are compared with those reported by existing methods. In addition, the convergence behavior of the proposed method is discussed through the consecutive errors. The results show that ISTT provides a simple iterative approach for obtaining approximate solutions of nonlinear coupled fractional differential equations.

This article focuses on the study of solid tumours, particularly malignant ones, through the use of sophisticated mathematical model aimed at explaining their growth, which is primarily driven by cellular proliferation. Among these, gliomas, one of the most severe forms of brain cancer, are notable for their distinct behaviour, marked by deep infiltration into surrounding tissues. We primarily focus on studying a specific type of glioma known as glioblastoma multiforme using the brain tumour growth model governed by the Burgess equation. To achieve this, we implement a hybrid numerical scheme which is combination of polynomial differential quadrature method and best four‐stage, third‐order strong stability‐preserving time‐stepping Runge–Kutta (SSP‐RK43) algorithm. The stability of the proposed method is also studied using matrix method. Moreover, the order of convergence of the proposed scheme is presented. The proposed scheme is simulated and tested on some test examples. We compare the results with the existing methods in terms of error. The computational time for each example is presented. The low computational cost demonstrates the efficiency of the proposed scheme.