论文标题
WALSH多项式方法的数值解决方案的数值解决方案的存在和独立性
The existence and unicity of numerical solution of initial value problems by Walsh polynomials approach
论文作者
论文摘要
Chen和Hsiao给出了通过WALSH多项式方法恒定系数的线性微分方程系统的初始值问题的数值解决方案。 Gát和Toledo改善了此结果，以解决间隔$ [0,1 [$和初始值$ξ= 0 $的微分方程的初始值问题。在本文中，我们讨论了一般案例，而$ξ$可以在间隔$ [0,1 [$的间隔中获取任何任意值。我们也显示了数值解的存在和统一收敛性。
Chen and Hsiao gave the numerical solution of initial value problems of systems of linear differential equations with constant coefficients by Walsh polynomials approach. This result was improved by Gát and Toledo for initial value problems of differential equations with variable coefficients on the interval $[0,1[$ and initial value $ξ=0$. In the present paper we discuss the general case while $ξ$ can take any arbitrary value in the interval $[0,1[$. We show the existence and uniform convergence of the numerical solution, as well.
