L-稳定块格式及其在隐式微分方程中的实现

Construction of L-Stability Block Methods and Implementation for Implicit Differential Equations

以指数函数的Padé逼近作为块格式的稳定函数,使用精度条件的理论——精度p的格式能精确求解解为不超过p次多项式的微分方程,以解的Taylor展式为基础,构造出L-稳定的块格式。并针对隐式微分方程进行实现,与常用的几种求解器进行了比较,结果表明构造的格式及其实现在效率上是优秀的。

Block methods were constructed with L-stability, using Pade approximations to the exponential function as stability function, and applying the theory that a method of order p is capable of solving any differential equation exactly if its solution is a polynomial of degree not exceeding p, and based on Taylor series. Implementation issues for implicit differential equations were proposed, and numerical experiments comparing this implementation with other well-known solvers were given. The results show that the solver turns out to be a robust and reliable one.