论文标题
stieltjes普通微分方程的近似
Approximation of Stieltjes ordinary differential equations
论文作者
论文摘要
这项工作专门用于获得基于正交公式的新数值方案，用于lebesgue-stieltjes积分，以近似stieltjes普通微分方程。这种新颖的方法使我们能够在基于stieltjes的普通微分方程中数值近似模型，该方程未知明确的解决方案。我们证明了与数值方法的一致性，收敛性和稳定性有关的几个理论结果。我们还获得了线性普通微分方程的明确解，并使用它来验证数值方法。最后，我们提出了一些基于stieltjes微分方程的现实种群模型获得的数值结果。
This work is devoted to the obtaining of a new numerical scheme based in quadrature formulas for the Lebesgue-Stieltjes integral for the approximation of Stieltjes ordinary differential equations. This novel method allows us to numerically approximate models based in Stieltjes ordinary differential equations for which no explicit solution is known. We prove several theoretical results related to the consistency, convergence and stability of the numerical method. We also obtain the explicit solution of the Stieltjes linear ordinary differential equation, and we use it to validate the numerical method. Finally, we present some numerical results that we have obtained for a realistic population model based in a Stieltjes differential equation.
