Abstract In this article, a numerical model for a Brusselator advection–reaction–diffusion (BARD) system by using an elegant numerical scheme is developed. The consistency and stability of the proposed scheme is demonstrated. Positivity preserving property of the proposed scheme is also verified. The designed scheme is compared with the two well-known existing classical schemes to validate the certain physical properties of the continuous system. A test problem is also furnished for simulations to support our claim. Prior to computations, the existence and uniqueness of solutions for more generic problems is investigated. In the underlying system, the nonlinearities depend not only on the desired solution but also on the advection term that reflects the pivotal importance of the study.

中文翻译：

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非线性对流-反应-扩散系统的新型数值分析

摘要 在本文中，使用优雅的数值方案开发了布鲁塞尔对流-反应-扩散 (BARD) 系统的数值模型。证明了所提出方案的一致性和稳定性。还验证了所提出方案的正性保持特性。将所设计的方案与现有的两个众所周知的经典方案进行比较，以验证连续系统的某些物理性质。还为模拟提供了一个测试问题以支持我们的主张。在计算之前，研究了更一般问题的解的存在性和唯一性。在底层系统中，非线性不仅取决于所需的解，还取决于反映研究关键重要性的平流项。