论文标题
线性微分方程的数值解，具有不连续系数和HENSTOCK积分
Numerical solution of linear differential equations with discontinuous coefficients and Henstock integral
论文作者
论文摘要
在本文中，我们考虑了线性微分方程的近似解决方案的问题$ y'+p（x）y = q（x）$，带有不连续系数$ p $和$ q $。我们假设此类方程的系数是HENSTOCK集成函数。为了找到近似解决方案，我们将原始的Cauchy问题更改为分段恒定系数的另一个问题。这个新问题的尖锐解决方案是原始库奇问题的近似解决方案。我们找到了从连续性$ω_δ（p），\ω_δ（q）$的模量的近似值，其中$ p $和$ q $是系数的$ f $ - p $ $ p $和$ q $。
In this article we consider the problem of approximative solution of linear differential equations $y'+p(x)y=q(x)$ with discontinuous coefficients $p$ and $q$. We assume that coefficients of such equation are Henstock integrable functions. To find the approximative solution we change the original Cauchy problem to another problem with piecewise-constant coefficients. The sharp solution of this new problems is the approximative solution of the original Cauchy problem. We find the degree approximation in terms of modulus of continuity $ω_δ(P),\ ω_δ(Q)$, where $P$ and $Q$ are $f$-primitive for coefficients $p$ and $q$.
