We present here asymptotic solutions of equations of the type , where is a large parameter. The Bessel differential equation is considered as a typical example of the above and the solutions are provided as . Furtherm...We present here asymptotic solutions of equations of the type , where is a large parameter. The Bessel differential equation is considered as a typical example of the above and the solutions are provided as . Furthermore, the behaviour of the solutions as well as the stability of the Bessel ode is investigated numerically as the parameter grows indefinitely.展开更多
This paper is concerned with the stability analysis of nonlinear third order ordinary differential equations of the form . We construct a suitable Lyapunov function for this purpose and show that it guarantees asympto...This paper is concerned with the stability analysis of nonlinear third order ordinary differential equations of the form . We construct a suitable Lyapunov function for this purpose and show that it guarantees asymptotic stability. Our approach is to first consider the linear version of the above ODE, by taking and study its Lyapunov stability. Exploiting the similarities between linear and nonlinear ODE, we construct a Lyapunov function for the stability analysis of the given nonlinear differential equation.展开更多
文摘We present here asymptotic solutions of equations of the type , where is a large parameter. The Bessel differential equation is considered as a typical example of the above and the solutions are provided as . Furthermore, the behaviour of the solutions as well as the stability of the Bessel ode is investigated numerically as the parameter grows indefinitely.
文摘This paper is concerned with the stability analysis of nonlinear third order ordinary differential equations of the form . We construct a suitable Lyapunov function for this purpose and show that it guarantees asymptotic stability. Our approach is to first consider the linear version of the above ODE, by taking and study its Lyapunov stability. Exploiting the similarities between linear and nonlinear ODE, we construct a Lyapunov function for the stability analysis of the given nonlinear differential equation.
