On the attainable order of collocation methods for pantograph integro-differential equations
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- 作者：Muroya ; Yoshiaki ; Ishiwata ; Emiko ; Brunner ; Hermann
- 关键词：65L60 ; 65L70 ; 34K28 ; Integro-differential equation ; Proportional delay ; Collocation method
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：2003
- 出版时间：March 1, 2003
- 年：2003
- 卷：152
- 期：1-2
- 页码：347-366
- 全文大小：226 K
文摘
For the pantograph integro-differential equation (PIDE) with nonhomogeneous term: Cannot display formula, with proportional delays σ(q)t and ρ(q)t,0<σ(q),ρ(q)≤1,0<q≤1, we consider the attainable order of m-stage implicit (collocation-based) Runge–Kutta methods at the first mesh point t=h, and give conditions on the collocation polynomials Mm(t) of degree m to v(th),t
[0,1] such that |v(h)−y(h)|=O(h2m+1), where y(t) is the solution and v(t) is the collocation solution of PIDE. If m=2 or f(t) is a polynomial of t whose degree is less than or equal to m, then such conditions of Mm(t) are simplified. A numerical example is also included.
[0,1] such that |v(h)−y(h)|=O(h2m+1), where y(t) is the solution and v(t) is the collocation solution of PIDE. If m=2 or f(t) is a polynomial of t whose degree is less than or equal to m, then such conditions of Mm(t) are simplified. A numerical example is also included.