جستجوی مقالات مرتبط با کلیدواژه « third order » در نشریات گروه « ریاضی »

In this work, a non-classical sinc-collocation method is used to  find numerical solution of third-order boundary value problems. The novelty of this approach is based on using the weight functions in the traditional sinc- expansion. The properties of sinc-collocation are used to reduce the boundary value problems to a nonlinear system of algebraic equations which can be solved numerically. In addition, the convergence of the proposed method is discussed by preparing the theorems which show exponential convergence and guarantee its applicability. Several examples are solved and the numerical results show the efficiency and applicability of the method.

This paper deals with the oscillatory and asymptotic properties of third-order semi-canonical difference equations with positive and negative terms of the form$$\Delta\left(\varphi(\ell)\Delta\left(\psi(\ell)\Delta \mu(\ell) \right) \right)+\xi(\ell)f(\mu(\sigma(\ell)))-\chi(\ell)g(\mu(\tau(\ell)))=0.$$Using a canonical transformation technique, we offer new criteria which imply that the solutions of the studied equation are almost oscillatory. Some examples are provided to support our results.

This work deals with the existence of periodic solutions (EPSs) to a third order nonlinear delay differential equation (DDE) with multiple constant delays. For the considered DDE, a theorem is proved, which includes sufficient criteria related to the EPSs. The technique of the proof depends on Lyapunov-Krasovskiˇı functional (LKF) approach. The obtained result extends and improves some results that can be found in the literature. In a particular case of the considered DDE, an example is provided to show the applicability of the main result of this paper.

A third-order fractional ordinary differential equation (FrODE) is very important in the mathematical modelling of physical problems. Generally, the third-order ODE is solved by converting the differential equation to a system of first-order ODEs. However, it is a lot more efficient in terms of accuracy, a number of function evaluations as well as computational time if the problem can be solved directly using numerical methods. In this paper, we are focused on the derivation of the direct numerical methods which are one, two and three-stage methods for solving third-order FrODEs. The RKD methods with two- and three stages for solving third-order ODEs are adapted for solving special third-order FrDEs. Numerical examples have been evaluated to show the effectiveness of the new methods compared with the analytical method. Numerical experiments are carried out to verify the accuracy and efficiency of the proposed methods. Applications of proposed methods are also presented which yield impressive results for the proposed and modified methods. The numerical solutions of the test problems using proposed methods agree well with the analytical solutions. From the numerical results obtained using proposed methods, we can conclude that the proposed methods in which derived or modified in this paper are very efficient.