变域抽象微分方程的近似解
Approximate solution to abstract differential equations with variable domain
AI总结：
针对具有变域无界算子系数的一阶抽象微分方程，提出一种基于向量值函数Duhamel积分推广的新指数收敛算法，将原问题转化为积分方程组并以指数精度逼近。
摘要：
针对具有变域无界算子系数的一阶抽象微分方程，提出了一种新的指数收敛算法。该算法基于向量值函数的Duhamel积分的推广。该技术将初始问题转化为一个积分方程组。然后以指数精度逼近该方程组。通过热传导边值问题的例子说明了理论结果。
英文摘要：
A new exponentially convergent algorithm is proposed for an abstract the first order differential equation with unbounded operator coefficient possessing a variable domain. The algorithm is based on a generalization of the Duhamel integral for vector-valued functions. This technique translates the initial problem to a system of integral equations. Then the system is approximated with exponential accuracy. The theoretical results are illustrated by examples associated with the heat transfer boundary value problems.
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