Boundedness properties in Volterra integro-differential systems

Characterizations of Positive Linear Volterra Integro-differential Systems

We first give a criterion for positivity of the solution semigroup of linear Volterra integro-differential systems. Then, we offer some explicit conditions under which the solution of a positive linear Volterra system is exponentially stable or (robustly) lies in L2[0,+∞). Mathematics Subject Classification (2000). Primary 34A30; Secondary 34K20.

Positive Solutions of Volterra Integro–differential Equations

We present some sufficient conditions such that Eq. (1) only has solutions with zero points in (0,∞). Moreover, we also obtain some conditions such that Eq. (1) has a positive solution on [0,+∞). The motivation of this work comes from the work of Ladas, Philos and Sficas [5]. They discussed the oscillation behavior of Eq. (1) when P (t, s) = P (t− s) and g(t) = t. They obtained a necessary and ...

Volterra integro-differential equations and infinite systems of ordinary differential equations

Analytical-Approximate Solution for Nonlinear Volterra Integro-Differential Equations

In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

SPLINE COLLOCATION FOR FREDHOLM AND VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toil...