A step-by-step approximation and analysis of asymptotic stability properties of solution of retarded system

  • DK Igobi
  • MO Egwurube

Abstract

The special transcendental character of the characteristic equations of the
retarded differential systems makes it difficult to analyze the system equation. Researchers have used various acceptable mathematical techniques to address the issue. In this paper, the convergent properties of an integral equation equivalent of a retarded system are used to establish the existence and uniqueness of the solution of retarded differential equations. A step-by-step approximating technique is employed in formulating a numerical method of solving an initial value problem of the retarded system and the solution is presented in the form of a finite series. The asymptotic stability properties of the solution are investigated. Results obtained are comparable to the general solution form of the ordinary differential equations
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