We develop the contour integral method for numerically solving the Feynman-Kac equation with two internal states [P. B. Xu and W. H. Deng, Math. Model. Nat. Phenom., 13 (2018), 10], describing the functional distribution of particle's internal states. The striking benefits are obtained, including spectral accuracy, low computational complexity, small memory requirement, etc. We perform the error estimates and stability analyses, which are confirmed by numerical experiments.

翻译：我们发展了用于数值求解具有两个内部态的Feynman-Kac方程[P. B. Xu and W. H. Deng, Math. Model. Nat. Phenom., 13 (2018), 10]的围道积分法，该方程描述了粒子内部态的函数分布。该方法获得了显著优势，包括谱精度、低计算复杂度和较小的内存需求等。我们进行了误差估计和稳定性分析，并通过数值实验加以验证。