We present a finite difference method for a system of two singularly perturbed initial-boundary value semilinear reaction–diffusion equations. The highest order derivatives are multiplied by small perturbation parameters of different magnitudes. The problem is discretized using a central difference scheme in space and backward difference scheme in time on a Shishkin mesh. The convergence analysis has been given, and it has been established that the method enjoys almost second-order parameter-uniform convergence in space and first-order in time. Numerical experiments are conducted to demonstrate the efficiency of the method.

中文翻译：

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两个奇异摄动的瞬态半线性反应-扩散方程系统的逐点误差估计

我们提出了一个系统的两个奇异摄动初始边界值半线性反应扩散方程的有限差分方法。最高阶导数乘以不同量级的小扰动参数。该问题在 Shishkin 网格上使用空间中心差分格式和时间后向差分格式离散化。给出了收敛性分析，确定该方法在空间上几乎是二阶参数一致收敛，在时间上是一阶收敛。进行了数值实验以证明该方法的有效性。