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 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.

A Galerkin-Type Method to Solve One-Dimensional Telegraph Equation Using Collocation Points in Initial and Boundary Conditions

2018 ◽  
Vol 15 (05) ◽  
pp. 1850031 ◽  
Author(s):  
Şuayip Yüzbaşı ◽  
Murat Karaçayır
Keyword(s):  
Approximate Solution ◽  
Boundary Conditions ◽  
Telegraph Equation ◽  
Inner Product ◽  
Present Scheme ◽  
One Dimensional ◽  
Collocation Points ◽  
Correction Technique ◽  
Initial And Boundary Conditions ◽  
Residual Correction

In this study, a Galerkin-type approach is presented in order to numerically solve one-dimensional hyperbolic telegraph equation. The method includes taking inner product of a set of bivariate monomials with a vector obtained from the equation in question. The initial and boundary conditions are also taken into account by a suitable utilization of collocation points. The resulting linear system is then solved, yielding a bivariate polynomial as the approximate solution. Additionally, the technique of residual correction, which aims to increase the accuracy of the approximate solution, is discussed briefly. The method and the residual correction technique are illustrated with four examples. Lastly, the results obtained from the present scheme are compared with other methods present in the literature.

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 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.

Solving Fractional Delay Differential Equations: A New Approach

2015 ◽  
Vol 18 (2) ◽  
Author(s):  
Varsha Daftardar-Gejji ◽  
Yogita Sukale ◽  
Sachin Bhalekar
Keyword(s):  
Differential Equations ◽  
Error Analysis ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
New Method ◽  
New Approach ◽  
Fractional Order Differential Equations ◽  
Fractional Delay ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

AbstractA new method to solve non-linear fractional-order differential equations involving delay has been presented. Applications to a variety of problems demonstrate that the proposed method is more accurate and time efficient compared to existing methods. A detailed error analysis has also been given.

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