钙离子作为第二信使在细胞内传播着信息和调节着多种细胞的功能，细胞内钙离子信号及其产生机理是目前研究热点之一。借助于数学模型在一定程度上重现细胞内钙离子的发展演化过程是研究钙信号的一种重要方法。对细胞内钙动力学数学模型进行数值模拟,并和实验结果比较,可以更好地解释数学模型,并为数学模型的进一步修正提供理论依据。本项目将应用具有高精度的谱方法及其区域分裂方法（谱元法）数值求解细胞内钙动力学数学模型，对于由偏微分方程描述细胞内钙动力学的一类数学模型问题，构造计算快捷、稳定性好的谱方法，并编制相应的应用软件；在理论上建立相应的数值分析框架，分析数值方法的后验误差估计，为细胞内钙动力学数学模型的数值求解提供新的强有力的工具，开拓谱方法新的应用领域。

Ca2+, serving as a second messenger, plays an important role in many physiological processes. It transmits information between cells as well as regulates diverse cellular functions. The research of the intracellular calcium signal and its dynamics has become one of hot topics. Mathematical modeling provides an important approach to reapear and investigate the evolution process of the intracellular Ca2+. By numerical simulation of the mathematical models and comparsion with experimental data we can not only see the inside of the mathematical models but also find better theoretical basics for improving the modeling. In the present project, we will use the high accuracy spectral method and its domain domecomposition method(spectral element method) to simulate the mathematical models of intracellular calcium dynamics. Particularly, for the mathematical models described by partial differential equations, we will construct the spectral method schemes with high-speed as well as good stability in computation,and program the corresponding application software. We hope to formulate the framework for the corresponding numerical analysis. We will analyze the posteriori error estimation of spectral element method,so that we could come up with a new and effective numerical method with high accuracy. The research will be helpful for investigating intracellular calcium dynamics and applying the spectral method to more fields.