کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4641392 | 1341307 | 2009 | 15 صفحه PDF | دانلود رایگان |
The problem that motivates the considerations here is the construction of mathematical models of natural phenomena that depend upon past states. The paper divides naturally into two parts: in the first, we expound the inter-connection between ordinary differential equations, delay-differential equations, neutral delay-differential equations and integral equations (with emphasis on certain linear cases). As we show, this leads to a natural hierarchy of model complexity when such equations are used in mathematical and computational modelling, and to the possibility of reformulating problems either to facilitate their numerical solution or to provide mathematical insight, or both. Volterra integral equations include as special cases the others we consider. In the second part, we develop some practical and theoretical consequences of results given in the first part. In particular, we consider various approaches to the definition of an adjoint, we establish (notably, in the context of sensitivity analysis for neutral delay-differential equations) rôles for well-defined adjoints and ‘quasi-adjoints’, and we explore relationships between sensitivity analysis, the variation of parameters formulae, the fundamental solution and adjoints.
Journal: Journal of Computational and Applied Mathematics - Volume 229, Issue 2, 15 July 2009, Pages 335–349