We propose an easy-to-implement iterative method for resolving the implicit (or semi-implicit) schemes arising in solving reaction-diffusion (RD) type equations. We formulate the nonlinear time implicit scheme as a min-max saddle point problem and then apply the primal-dual hybrid gradient (PDHG) method. Suitable precondition matrices are applied to the PDHG method to accelerate the convergence of algorithms under different circumstances. Furthermore, our method is applicable to various discrete numerical schemes with high flexibility. From various numerical examples tested in this paper, the proposed method converges properly and can efficiently produce numerical solutions with sufficient accuracy.

翻译：我们提出了一种易于实现的迭代方法，用于求解反应扩散（RD）类型方程中出现的隐式（或半隐式）格式。将非线性时间隐式格式表述为一个极小-极大鞍点问题，进而应用原始-对偶混合梯度（PDHG）方法。针对不同情形，对PDHG方法施加合适的预条件矩阵以加速算法收敛。此外，本方法具有高度灵活性，可适用于各种离散数值格式。通过本文测试的多个数值算例表明，所提方法能正确收敛，并高效生成具有足够精度的数值解。