Frontiers of Mathematics in China >
On collocation methods for delay differential and Volterra integral equations with proportional delay
Received date: 02 Jul 2008
Accepted date: 22 Oct 2008
Published date: 05 Mar 2009
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To compute long term integrations for the pantograph differential equation with proportional delay qt, 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 order p∗ = 2m for computing long term integrations. Numerical investigations for these methods are also presented.
Emiko ISHIWATA , Yoshiaki MUROYA . On collocation methods for delay differential and Volterra integral equations with proportional delay[J]. Frontiers of Mathematics in China, 2009 , 4(1) : 89 -111 . DOI: 10.1007/s11464-009-0004-x
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