Numerical solution for a family of delay functional differential equations using step by step Tau approximations
Journal Title: Bulletin of Computational Applied Mathematics (Bull CompAMa) - Year 2013, Vol 1, Issue 2
Abstract
We use the segmented formulation of the Tau method to approximate the solutions of a family of linear and nonlinear neutral delay differential equations \begin{eqnarray} \nonumber a_1(t)y'(t) & = & y(t)[a_2(t)y(t-\tau)+a_3(t)y'(t-\tau) + a_4(t)] \\ \nonumber & & + \; a_5(t)y(t-\tau) + a_6(t)y'(t-\tau)+ a_7(t), \;\;\; t\geq 0 \\ \nonumber y(t) & = & \Psi(t),\;\;\;\; t\leq 0 \nonumber \end{eqnarray} which represents, for particular values of $a_i(t)$, $i=1,7$, and $\tau$, functional differential equations that arise in a natural way in different areas of applied mathematics. This paper means to highlight the fact that the step by step Tau method is a natural and promising strategy in the numerical solution of functional differential equations.
Authors and Affiliations
René Escalante
Keywords
Related Articles
- EP ID EP245541
- DOI -
- Views 74
- Downloads 0
Sparse approximations of matrix functions via numerical integration of ODEs
We consider the numerical computation of matrix functions f(x) via matrix ODE integration. The solution is modeled as an asymptotic steady state of a proper differential system. The framework we propose, allows to define...
Total dominator chromatic number of some operations on a graph
Let <i>G</i> be a simple graph. A total dominator coloring of <i>G</i> is a proper coloring of the vertices of <i>G</i> in which each vertex of the graph is adjacent to every vertex of some color class. The total dominat...
Numerical solution of mixed Volterra-Fredholm integral equations using iterative method via two-variables Bernstein polynomials
This paper is concerned with the numerical solution of mixed Volterra-Fredholm integral equations, based on iterative method and two variable Bernstein polynomials. In the main result, this method has several benefits in...
Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems
We address the issue of approximating the pseudoinverse of the coefficient matrix for dynamically building preconditioning strategies for the numerical solution of large dense linear least-squares problems. The new prec...
Integrating Fuzzy Formal Concept Analysis and Rough Set Theory for the Semantic Web
Formal Concept Analysis and Rough Set Theory provide two mathematical frameworks in information management which have been developed almost independently in the past. Currently, their integration is revealing very intere...