Search

Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDEs) and build the classical stability, consistency, and convergence theories of the methods. The methods and theories presented in this paper are applicable to nonneutral, nonstiff, and nonlinear initial value problems in ODEs, Volterra delay differential equations (VDDEs), Volterra integro-differential equations (VIDEs), Volterra delay integro-differential equations (VDIDEs), etc. At last, some numerical experiments verify the correctness of our theories. [ABSTRACT FROM AUTHOR]

The article presents information on a study which investigated the global behavior of the difference equation of higher order. It notes that although difference equations are relatively simple in form, it is, unfortunately, extremely difficult to understand thoroughly the global behavior of their solutions. It describes difference equations as discrete analogues and as numerical solutions of differential and delay differential equations having applications in various scientific branches, such as in ecology, economy, physics, technics, sociology, and biology.

The article investigates a delayed stage-structured Ivlev's functional response predator-prey model with continuous harvesting on predator and impulsive stocking on prey. It examines the condigions of the global attractivity of predator-extinction periodic solution and the permanence of the system. The findings indicate the important role of the behavior of impulsive stocking on prey for the performance of the system. According to the authors, the results offer reliable tactical basis for the biological resource management and enrich the theory of impulsive delay differential equations.