二嵌段共聚物是共聚物中的一类，相比于均聚物，二嵌段共聚物会表现出微相分离现象. 微相分离现象对于在二嵌段共聚物的模拟以及对于生物、化学等方面的应用有理论的指导意义.

Otha-Kawasaki 模型用于模拟二嵌段共聚物. 通过谱方法将物质演化的偏 微分方程转化为常微分方程. 这类常微分方程带有刚性，通过一般的显式线性方法需要取较小步长才能使得算法稳定. 指数积分方法对于刚性的常微分方程求解有较好的效果. 本文对指数积分方法和谱方法的实现和原理进行介绍. 在此基础上，本文通过指数积分法来求解Otha-Kawasaki模型产生的常微分方程，给出了数值模拟结果，并且对其守恒性和能量下降的性质进行了验证.

Diblock copolymers are a class of copolymers that exhibit microphase segregation compared to homopolymers. The microphase separation phenomenon has theoretical implications for the simulation of diblock copolymers and for biological and chemical applications.

Otha-Kawasaki model for simulating diblock copolymers. The partial differential equations for the evolution of matter are transformed into ordinary difffferential equations by spectral methods. These ordinary difffferential equations are stiffff and require small step sizes to make the algorithm stable by the usual explicit linear methods. The exponential integration method has better results for the solution of stiff ordinary difffferential equations. In this paper, the implementation and principles of the exponential integration method and the spectral method are introduced. On this basis, this paper solves the ordinary difffferential equations generated by Otha-Kawasakimodel by the exponential integration method, gives numerical simulation results, and verififies its conservation and energy-drop properties.