DEVELOPMENT OF STIFF PDE SOLVERS IN VCELL

该子项目是利用 由NIH/NCRR资助的中心赠款提供的资源。子项目和 研究者（PI）可能从另一个NIH来源获得主要资金， 因此可以在其他CRISP条目中表示。列出的机构是 中心，不一定是研究者的机构。 算法将被实现，这将有效地科普可能出现的机制的刚度  反应和膜通量-由用户指定，因此事先不知道。最后，算法应该尽可能的“交钥匙”，以减轻生物用户作出决定的时间步长的数值积分。将开发在存在巨大不同的时间尺度的情况下具有稳定性能的PDE解算器（解算器），其将在给定公差内自动产生解决方案（设置为实现合理的生物应用精度）。生物学应用的特定要求之一是求解器应该足够快。我们将追求顺序算法的基础上，操作分裂的思想与改进的时间离散化误差。

This subproject is one of many research subprojects utilizing the resources provided by a Center grant funded by NIH/NCRR. The subproject and investigator (PI) may have received primary funding from another NIH source, and thus could be represented in other CRISP entries. The institution listed is for the Center, which is not necessarily the institution for the investigator. Algorithms will be implemented that will cope effectively with stiffness that may arise from the mechanisms  reactions and membrane fluxes - that are specified by the user and, therefore, are not known in advance. Ultimately, the algorithms should be as "turn-key" as possible in order to relieve a biological user of making a decision about the time step of numerical integration. A PDE solver (solvers) with a stable performance in the presence of vastly different time scales will be developed that, which will automatically produce a solution within a given tolerance (set to achieve a reasonable for biological applications accuracy). One of the requirements specific for biological applications is that the solver should be sufficiently fast. We will pursue sequential algorithms based on the idea of operator splitting with an improved time discretization error.