Laguerre matrix method with the residual error estimation for solutions of a class of delay differential equations

2013 ◽  
Vol 37 (4) ◽  
pp. 453-463 ◽  
Author(s):  
Şuayip Yüzbaşı ◽  
Emrah Gök ◽  
Mehmet Sezer
Keyword(s):  
Differential Equations ◽  
Error Estimation ◽  
Delay Differential Equations ◽  
Matrix Method ◽  
Residual Error ◽  
Delay Differential

scholarly journals Application of Vieta–Lucas Series to Solve a Class of Multi-Pantograph Delay Differential Equations with Singularity

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2370
Author(s):  
Mohammad Izadi ◽  
Şuayip Yüzbaşı ◽  
Khursheed J. Ansari
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Error Estimation ◽  
Delay Differential Equations ◽  
Numerical Test ◽  
Estimation Technique ◽  
Residual Function ◽  
Collocation Approach ◽  
Collocation Scheme ◽  
Delay Differential

The main focus of this paper was to find the approximate solution of a class of second-order multi-pantograph delay differential equations with singularity. We used the shifted version of Vieta–Lucas polynomials with some symmetries as the main base to develop a collocation approach for solving the aforementioned differential equations. Moreover, an error bound of the present approach by using the maximum norm was computed and an error estimation technique based on the residual function is presented. Finally, the validity and applicability of the presented collocation scheme are shown via four numerical test examples.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

Mass Transport Modelling in Porous Media Using Delay Differential Equations

2006 ◽  
Vol 258-260 ◽  
pp. 586-591
Author(s):  
António Martins ◽  
Paulo Laranjeira ◽  
Madalena Dias ◽  
José Lopes
Keyword(s):  
Porous Media ◽  
Differential Equations ◽  
Mass Transport ◽  
Delay Differential Equations ◽  
Dispersion Model ◽  
Flow Characteristics ◽  
Convective Transport ◽  
Transport Modelling ◽  
Flow Field Characteristics ◽  
Delay Differential

In this work the application of delay differential equations to the modelling of mass transport in porous media, where the convective transport of mass, is presented and discussed. The differences and advantages when compared with the Dispersion Model are highlighted. Using simplified models of the local structure of a porous media, in particular a network model made up by combining two different types of network elements, channels and chambers, the mass transport under transient conditions is described and related to the local geometrical characteristics. The delay differential equations system that describe the flow, arise from the combination of the mass balance equations for both the network elements, and after taking into account their flow characteristics. The solution is obtained using a time marching method, and the results show that the model is capable of describing the qualitative behaviour observed experimentally, allowing the analysis of the influence of the local geometrical and flow field characteristics on the mass transport.

Sign in / Sign up

Export Citation Format

Share Document