On collocation methods for delay differential and Volterra integral equations with proportional delay
On collocation methods for delay differential and Volterra integral equations with proportional delay
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DOI：
10.1007/s11464-009-0004-x
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发表时间：
2009-02
影响因子：
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通讯作者：
E. Ishiwata;Y. Muroya
中科院分区：
文献类型：
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作者：
E. Ishiwata;Y. Muroya
为了计算具有比例延迟 qt 的受电弓微分方程 0 <q⩽ 1:y′(t) =ay(t) +by(qt) +f(t),y(0) =y0，我们提供了两种使用特殊网格分布的数值方法，即具有“准均匀网格”的有理近似法（参见 E. Ishiwata 和 Y. Muroya [Appl. 数学。 Comput., 2007, 187: 741-747]）和具有“准约束网格”的高斯配置方法。如果我们分别将这些网格应用于有理逼近法和高斯配置法，那么我们将获得用于计算长期积分的有用的 p*= 2m 阶数值方法。还介绍了这些方法的数值研究。
To compute long term integrations for the pantograph differential equation with proportional delayqt, 0 <q⩽ 1:y′(t) =ay(t) +by(qt) +f(t),y(0) =y0, we offer two kinds of numerical methods using special mesh distributions, that is, a rational approximant with ‘quasi-uniform meshes’ (see E. Ishiwata and Y. Muroya [Appl. Math. Comput., 2007, 187: 741-747]) and a Gauss collocation method with ‘quasi-constrained meshes’. If we apply these meshes to rational approximant and Gauss collocation method, respectively, then we obtain useful numerical methods of orderp*= 2mfor computing long term integrations. Numerical investigations for these methods are also presented.