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Numerical Solution for Brain Tumour Model Using an Efficient Technique
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DOI：10.1002/adts.202501661.png)
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Abstract
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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.
Keywords:
brain tumour model
numerical method
polynomial differential quadrature method
Runge-Kutta method
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