A directly convergent numerical method based on orthoexponential polynomials for solving integro-differential-delay equations with variable coefficients and infinite boundary on half-line

2021 ◽  
Vol 386 ◽  
pp. 113250
Author(s):  
Ömür Kıvanç Kürkçü ◽  
Mehmet Sezer
Keyword(s):  
Numerical Method ◽  
Variable Coefficients ◽  
Delay Equations ◽  
Half Line ◽  
Differential Delay ◽  
Differential Delay Equations

scholarly journals A numerical method with a control parameter for integro-differential delay equations with state-dependent bounds via generalized Mott polynomial

2019 ◽  
Vol 14 (1) ◽  
pp. 43-52
Author(s):  
Ömür Kıvanç Kürkçü
Keyword(s):  
Numerical Method ◽  
Present Method ◽  
Phase Plane ◽  
Delay Equations ◽  
Mathematical Software ◽  
Program Module ◽  
Differential Delay ◽  
Differential Delay Equations ◽  
Collocation Points ◽  
State Dependent

AbstractIn this paper, we introduce a numerical method to obtain an accurate approximate solution of the integro-differential delay equations with state-dependent bounds. The method is based basically on the generalized Mott polynomial with the parameter-$$\beta$$β, Chebyshev–Lobatto collocation points and matrix structures. These matrices are gathered under a unique matrix equation and then solved algebraically, which produce the desired solution. We discuss the behavior of the solutions, controlling their parameterized form via $$\beta$$β and so we monitor the effectiveness of the method. We improve the obtained solutions by employing the Mott-residual error estimation. In addition to comparing the results in tables, we also illustrate the solutions in figures, which are made up of the phase plane, logarithmic and standard scales. All results indicate that the present method is simple-structured, reliable and straightforward to write a computer program module on any mathematical software.

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