Chelyshkov collocation method for a class of mixed functional integro-differential equations

Oğuz, Cem; Sezer, Mehmet

doi:10.1016/j.amc.2015.03.024

“…Eventually, in order to find the Lucas polynomial solution of the problem (1)-(2), by replacing m row matrices (16) into any m rows of the form (15). Thus, we have the augmented matrix…”

Section: Lucas Matrix-collocation Techniquementioning

confidence: 99%

“…In this paper, by considering the matrix technique based on collocation points, which have been used by Sezer and coworkers [5,6,[8][9][10][11][12][13][14][15][16][17][18][19], we purpose a new numerical technique to find an approximate solution of the problem (1)- (2). The solution is of the form…”

Section: Introductionmentioning

confidence: 99%

A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays

Gümgüm

¹

,

Savaşaneril

²

,

Kürkçü

³

et al. 2018

Sakarya University Journal of Science

Self Cite

View full text Add to dashboard Cite

In this paper, a new numerical matrix-collocation technique is considered to solve functional integrodifferential equations involving variable delays under the initial conditions. This technique is based essentially on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points. Some descriptive examples are performed to observe the practicability of the technique and the residual error analysis is employed to improve the obtained solutions. Also, the numerical results obtained by using these collocation points are compared in tables and figures.

show abstract

“…However, most of the mentioned type delay equations have not analytical and numerical solutions; therefore, numerical methods are required to obtain approximate solutions. For this purpose, by means of the matrix method based on collocation points which have been given by Sezer and coworkers [2,6,16,17,21,26,29,36], we develop a novel matrix technique to find the approximate solution of Eq. 1 under the initial condition yðaÞ ¼ k in the truncated Morgan-Voyce series form…”

Section: Introductionmentioning

confidence: 99%

A numerical approach for a nonhomogeneous differential equation with variable delays

Özel

¹

,

Tarakçı

²

,

Sezer

³

2018

Self Cite

View full text Add to dashboard Cite

In this study, we consider a linear nonhomogeneous differential equation with variable coefficients and variable delays and present a novel matrix-collocation method based on Morgan-Voyce polynomials to obtain the approximate solutions under the initial conditions. The method reduces the equation with variable delays to a matrix equation with unknown MorganVoyce coefficients. Thereby, the solution is obtained in terms of Morgan-Voyce polynomials. In addition, two test problems together with error analysis are performed to illustrate the accuracy and applicability of the method; the obtained results are scrutinized and interpreted by means of tables and figures.

show abstract

“…However, most of the mentioned type delay equations have not analytical and numerical solutions; therefore, numerical methods are required to obtain approximate solutions. For this purpose, by means of the matrix method based on collocation points which have been given by Sezer and coworkers [2,6,16,17,21,26,29,36], we develop a novel matrix technique to find the approximate solution of Eq. 1 under the initial condition yðaÞ ¼ k in the truncated Morgan-Voyce series form y t ð Þ ffi y N t ð Þ ¼ X N n¼0 y n b n ðtÞ; a t b ð2Þ…”

Section: Introductionmentioning

confidence: 99%

The polynomial automorphisms of some certain groups

Askari¹,

Fattahi²

2013

Mathematical Sciences

0

View full text Add to dashboard Cite

In this study, we consider a linear nonhomogeneous differential equation with variable coefficients and variable delays and present a novel matrix-collocation method based on Morgan-Voyce polynomials to obtain the approximate solutions under the initial conditions. The method reduces the equation with variable delays to a matrix equation with unknown MorganVoyce coefficients. Thereby, the solution is obtained in terms of Morgan-Voyce polynomials. In addition, two test problems together with error analysis are performed to illustrate the accuracy and applicability of the method; the obtained results are scrutinized and interpreted by means of tables and figures.

show abstract

Chelyshkov collocation method for a class of mixed functional integro-differential equations

Cited by 40 publications

References 37 publications

A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays

A numerical technique based on Lucas polynomials together with standard and Chebyshev-Lobatto collocation points for solving functional integro-differential equations involving variable delays

A numerical approach for a nonhomogeneous differential equation with variable delays

The polynomial automorphisms of some certain groups

Contact Info

Product

Resources

About