Utilization of Chebyshev collocation approach for differential, differential-difference and integro-differential equations

Numerical solutions to differential and integral equations have been a very active field of research. The necessary tools to solving differential equations can add much fuel for acceleration of scientific development. Therefore, it is quite challenging for scientists, especially mathematicians, to w...

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Autores principales:	Hajra Zeb, Muhammad Sohail, Hussam Alrabaiah, Tahir Naseem
Formato:	article
Lenguaje:	EN
Publicado:	Taylor & Francis Group 2021
Materias:	collocation approach mathematical modelling numerical solution differential equation integro-differential equation differential-difference equation Science Q
Acceso en línea:	https://doaj.org/article/add633c96e204422a146344866392423
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spelling	oai:doaj.org-article:add633c96e204422a1463448663924232021-11-11T14:23:43ZUtilization of Chebyshev collocation approach for differential, differential-difference and integro-differential equations2576-529910.1080/25765299.2021.1997442https://doaj.org/article/add633c96e204422a1463448663924232021-01-01T00:00:00Zhttp://dx.doi.org/10.1080/25765299.2021.1997442https://doaj.org/toc/2576-5299Numerical solutions to differential and integral equations have been a very active field of research. The necessary tools to solving differential equations can add much fuel for acceleration of scientific development. Therefore, it is quite challenging for scientists, especially mathematicians, to work on the solution methodologies for differential equations. In this study, we have discussed the use of Chebyshev collocation method for solving a large variety of problems including various types of integral equations, integro-differential equations, and differential-difference equations. The method under consideration relies on a trial solution which is a linear combination of basic functions derived from Chebyshev polynomials. The trial solution is then used to obtain a residue function whose vanishing weighted residual can be used to obtain a system of algebraic equations which gives the values of constants used in the trial solution. Plugging the constants back into the trial solution, we obtain an approximate solution to the problem at hand. We have provided the comparison between exact and approximate solutions for different problems and found an exceptionally good agreement in results. The comparison has been provided through plots and tables to portray the accurateness of Chebyshev collocation method. The behaviour of the solutions is also displayed with the help of the graphs.Hajra ZebMuhammad SohailHussam AlrabaiahTahir NaseemTaylor & Francis Grouparticlecollocation approachmathematical modellingnumerical solutiondifferential equationintegro-differential equationdifferential-difference equationScienceQENArab Journal of Basic and Applied Sciences, Vol 28, Iss 1, Pp 413-426 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	collocation approach mathematical modelling numerical solution differential equation integro-differential equation differential-difference equation Science Q
spellingShingle	collocation approach mathematical modelling numerical solution differential equation integro-differential equation differential-difference equation Science Q Hajra Zeb Muhammad Sohail Hussam Alrabaiah Tahir Naseem Utilization of Chebyshev collocation approach for differential, differential-difference and integro-differential equations
description	Numerical solutions to differential and integral equations have been a very active field of research. The necessary tools to solving differential equations can add much fuel for acceleration of scientific development. Therefore, it is quite challenging for scientists, especially mathematicians, to work on the solution methodologies for differential equations. In this study, we have discussed the use of Chebyshev collocation method for solving a large variety of problems including various types of integral equations, integro-differential equations, and differential-difference equations. The method under consideration relies on a trial solution which is a linear combination of basic functions derived from Chebyshev polynomials. The trial solution is then used to obtain a residue function whose vanishing weighted residual can be used to obtain a system of algebraic equations which gives the values of constants used in the trial solution. Plugging the constants back into the trial solution, we obtain an approximate solution to the problem at hand. We have provided the comparison between exact and approximate solutions for different problems and found an exceptionally good agreement in results. The comparison has been provided through plots and tables to portray the accurateness of Chebyshev collocation method. The behaviour of the solutions is also displayed with the help of the graphs.
format	article
author	Hajra Zeb Muhammad Sohail Hussam Alrabaiah Tahir Naseem
author_facet	Hajra Zeb Muhammad Sohail Hussam Alrabaiah Tahir Naseem
author_sort	Hajra Zeb
title	Utilization of Chebyshev collocation approach for differential, differential-difference and integro-differential equations
title_short	Utilization of Chebyshev collocation approach for differential, differential-difference and integro-differential equations
title_full	Utilization of Chebyshev collocation approach for differential, differential-difference and integro-differential equations
title_fullStr	Utilization of Chebyshev collocation approach for differential, differential-difference and integro-differential equations
title_full_unstemmed	Utilization of Chebyshev collocation approach for differential, differential-difference and integro-differential equations
title_sort	utilization of chebyshev collocation approach for differential, differential-difference and integro-differential equations
publisher	Taylor & Francis Group
publishDate	2021
url	https://doaj.org/article/add633c96e204422a146344866392423
work_keys_str_mv	AT hajrazeb utilizationofchebyshevcollocationapproachfordifferentialdifferentialdifferenceandintegrodifferentialequations AT muhammadsohail utilizationofchebyshevcollocationapproachfordifferentialdifferentialdifferenceandintegrodifferentialequations AT hussamalrabaiah utilizationofchebyshevcollocationapproachfordifferentialdifferentialdifferenceandintegrodifferentialequations AT tahirnaseem utilizationofchebyshevcollocationapproachfordifferentialdifferentialdifferenceandintegrodifferentialequations
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Utilization of Chebyshev collocation approach for differential, differential-difference and integro-differential equations

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