间断系数线性微分方程的数值解与Henstock积分
Numerical solution of linear differential equations with discontinuous coefficients and Henstock integral
摘要：
本文考虑具有间断系数$p$和$q$的线性微分方程$y'+p(x)y=q(x)$的近似解问题。我们假设这类方程的系数是Henstock可积函数。为了找到近似解，我们将原来的柯西问题转化为另一个分段常系数问题。新问题的精确解是原Cauchy问题的近似解。我们发现的程度近似的连续模$ω_δ(P),\ ω_δ(Q)$，其中$P$和$Q$是$f$ -原始的系数$p$和$q$。
英文摘要：
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 $q$.
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