Numerical solution of retarded functional differential equations as abstract Cauchy problems

Numerical solution of constant coefficient linear delay differential equations as abstract Cauchy problems

In this paper we present an approach for the numerical solution of Delay Di erential Equations y 0 (t) = Ly (t) +My (t ) t 0 y (t) = ' (t) t 0; (1) where > 0, L;M 2 C I m m and ' 2 C ([ ; 0] ; C I m ), di erent from the classical step-by-step method. We restate (1) as an abstract Cauchy problem and then we discretize it in a system of Ordinary Differential Equations. The scheme of discretizatio...

The Numerical Solution of Delay-differential-algebraic Equations of Retarded

In this paper we consider the numerical solution of initial-value delay-differentialalgebraic equations (DDAEs) of retarded and neutral types, with a structure corresponding to that of Hessenberg DAEs. We give conditions under which the DDAE is well conditioned and show how the DDAE is related to an underlying retarded or neutral delay-ordinary differential equation (DODE). We present convergen...

Numerical Solution of Singular Integro-differential Equations with Cauchy Kernel

The main purpose of this article is to present an approximation method of for singular integrodifferential equations with Cauchy kernel in the most general form under the mixed conditions in terms of the second kind Chebyshev polynomials. This method transforms mixed singular integro-differential equations with Cauchy kernel and the given conditions into matrix equation and using the zeroes of ...

Abstract Cauchy problems and stochastic integral equations

Cauchy problems and stochastic integral equations Bachelor thesis, June 21, 2011 Thesis supervisor: dr. O. van Gaans Mathematisch Instituut, Universiteit Leiden

Numerical Solution of Differential Equations