scholarly journals On the stability and boundedness of certain third order non-autonomous differential equations of retarded type

2015 ◽  
Vol 34 (2) ◽  
pp. 147-159 ◽  
Author(s):  
Cemil Tunc
Keyword(s):  
Differential Equations ◽  
Third Order ◽  
The Stability ◽  
Autonomous Differential Equations

scholarly journals An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lee Ken Yap ◽  
Fudziah Ismail ◽  
Norazak Senu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Film Flow ◽  
Direct Solution ◽  
Thin Film Flow ◽  
Block Method ◽  
Third Order ◽  
Block Form ◽  
The Stability

The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form to provide the approximation at five points concurrently. The stability properties of the block method are investigated. Some numerical examples are tested to illustrate the efficiency of the method. The block hybrid collocation method is also implemented to solve the nonlinear Genesio equation and the problem in thin film flow.

scholarly journals On the stability and boundedness of solutions of nonlinear third order differential equations with delay

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 1-10 ◽  
Author(s):  
Cemil Tunç
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Relevant Literature ◽  
Stability Result ◽  
Boundedness Of Solutions ◽  
Third Order ◽  
Functional Differential ◽  
The Stability ◽  
Equations With Delay

By defining a Lyapunov functional, we investigate the stability and boundedness of solutions to nonlinear third order differential equation with constant delay, r : x'''(t) + g(x(t), x'(t))x''(t) + f (x(t - r), x'(t - r)) + h(x(t - r)) = p(t, x(t), x'(t), x(t - r), x'(t - r), x''(t)), when p(t, x(t), x'(t), x(t - r), x'(t - r), x''(t)) = 0 and ? 0, respectively. Our results achieve a stability result which exists in the relevant literature of ordinary nonlinear third order differential equations without delay to the above functional differential equation for the stability and boundedness of solutions. An example is introduced to illustrate the importance of the results obtained.

Sign in / Sign up

Export Citation Format

Share Document