We present a finite volume method preserving the invariant region property (IRP) for the reaction-diffusion systems with quasimonotone functions, including nondecreasing, decreasing, and mixed quasimonotone systems. The diffusion terms and time derivatives are discretized by a finite volume method satisfying the discrete maximum principle (DMP) and the backward Euler method, respectively. The discretization leads to an implicit and nonlinear scheme, and it is proved to preserve the invariant region property unconditionally. We construct an iterative algorithm and prove the invariant region property ar each iteration step. Numerical examples are shown to confirm the accuracy and invariant region property of our scheme.

翻译：本文针对具有拟单调函数的反应-扩散系统（包括非递减、递减及混合拟单调系统），提出一种保持不变区域性质（IRP）的有限体积法。扩散项采用满足离散极大值原理（DMP）的有限体积法离散，时间导数则通过后向欧拉方法处理。该离散化产生一个隐式非线性格式，并证明该格式无条件保持不变区域性质。我们构建了一种迭代算法，并证明每一步迭代均保持不变区域性质。数值算例验证了该格式的精度及不变区域保持特性。