This article concerns with the numerical investigations of the reaction–diffusion systems (RDSs) arising in the study of pattern formation in biological and chemical systems with the employment of the quartic-trigonometric B-spline functions. The computationally numerical scheme uses collocation method which is established by a relatively new B-splines for the spatial discretizations and, for time integration Crank–Nicolson technique is adapted. Therefore, solutions of the RDSs are assembled by the wholly discretized space-time scheme. A matrix stability analysis is performed for the numerical scheme after linearization process. Experimental cases include Brusselator model, Gray–Scott model, Schnakenberg model as well as a linear problem in one-dimensional domain. Numerical solutions are compared to the existing studies. Spatial pattern formation is demonstrated by present computational algorithm.

本文涉及利用四次三角B样条函数研究生物和化学系统中的图案形成过程中发生的反应扩散系统（RDSs）的数值研究。计算数值方案使用并置方法，该方法由相对较新的B样条建立，用于空间离散化，并且为了进行时间积分，采用了Crank-Nicolson技术。因此，RDS的解决方案是通过完全离散的时空方案组合而成的。线性化过程后，对数值方案进行矩阵稳定性分析。实验案例包括Brusselator模型，Gray–Scott模型，Schnakenberg模型以及一维域的线性问题。将数值解与现有研究进行了比较。