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.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

Computational Treatment of First Order Delay Differential Equations Using Hybrid Extended Second Derivative Block Backward Differentiation Formulae

2020 ◽  
Vol 1 (1) ◽  
Author(s):  
C. Chibuisi ◽  
Bright Okore Osu ◽  
C. Olunkwa ◽  
S. A. Ihedioha ◽  
S. Amaraihu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Derivative ◽  
Delay Term ◽  
First Order ◽  
Block Form ◽  
Collocation Approach ◽  
Backward Differentiation Formulae ◽  
Delay Differential ◽  
Step Number

This paper considers the computational solution of first order delay differential equations (DDEs) using hybrid extended second derivative backward differentiation formulae method in block form without the implementation of interpolation techniques in estimating the delay term. By matrix inversion approach, the discrete schemes were obtained through the linear multistep collocation approach from the continuous form of each step number which after implementation strongly revealed the convergence and region of absolute stability of the proposed method. Computational results are presented and compared to the exact solutions and other existing method to demonstrate its efficiency and accuracy.

scholarly journals Computer simulation of pantograph delay differential equations

2021 ◽  
pp. 37-37
Author(s):  
Xian-Yong Liu ◽  
Yan-Ping Liu ◽  
Zeng-Wen Wu
Keyword(s):  
Computer Simulation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Integral Equations ◽  
Delay Differential Equations ◽  
Ritz Method ◽  
Variational Theory ◽  
Unknown Parameters ◽  
Trial Solution ◽  
Delay Differential

Ritz method is widely used in variational theory to search for an approximate solution. This paper suggests a Ritz-like method for integral equations with an emphasis of pantograph delay equations. The unknown parameters involved in the trial solution can be determined by balancing the fundamental terms.

scholarly journals A Galerkin-like approach to solve multi-pantograph type delay differential equations

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 409-422 ◽  
Author(s):  
Şuayip Yüzbaşı ◽  
Murat Karaçayır
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Error Analysis ◽  
Delay Differential Equations ◽  
Inner Product ◽  
Method Error ◽  
Correction Technique ◽  
Residual Correction ◽  
Delay Differential

In this paper, a Galerkin-like approach is presented to numerically solve multi-pantograph type delay differential equations. The method includes taking inner product of a set of monomials with a vector obtained from the equation under consideration. The resulting linear system is then solved, yielding a polynomial as the approximate solution. We also provide an error analysis and discuss the technique of residual correction, which aims to increase the accuracy of the approximate solution. Lastly, the method, error analysis and the residual correction technique are illustrated with several examples. The results are also compared with numerous existing methods from the literature.

scholarly journals Modified Laguerre wavelet based Galerkin method for fractional and fractional-order delay differential equations

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 13-21 ◽  
Author(s):  
Aydin Secer ◽  
Neslihan Ozdemir
Keyword(s):  
Approximate Solution ◽  
Integral Operator ◽  
Differential Equations ◽  
Galerkin Method ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Fractional Integral ◽  
Approximate Solutions ◽  
Delay Differential ◽  
The Given

The application of modified Laguerre wavelet with respect to the given conditions by Galerkin method to an approximate solution of fractional and fractional-order delay differential equations is studied in this paper. For the concept of fractional derivative is used Caputo sense by using Riemann-Liouville fractional integral operator. The presented method here is tested on several problems. The approximate solutions obtained by presented method are compared with the exact solutions and is shown to be a very efficient and powerful tool for obtaining approximate solutions of fractional and fractional-order delay differential equations. Some tables and figures are presented to reveal the performance of the presented method.

scholarly journals Numerical Solution of Fuzzy Multiple Hybrid Single Retarded Delay Differential Equations

2019 ◽  
Vol 8 (3) ◽  
pp. 1946-1949
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Exact Solutions ◽  
Numerical Solution ◽  
Hybrid Systems ◽  
Delay Differential Equations ◽  
Fuzzy Systems ◽  
Numerical Solutions ◽  
Delay Systems ◽  
Delay Differential

In this Paper, We are combining so many mathematical-cum-engineering topics such as Fuzzy systems, Delay systems and Hybrid Systems under one roof called Numerical Solutions. The fuzzy valued problem was solved numerically and that approximate solution was compared with that of exact solutions. The non fuzzy and fuzzy valued numerical solutions and their graphical illustrations are also provided for the better understanding of the multiple hybrid single retarded delay problems.

Sign in / Sign up

Export Citation Format

Share Document