Approximate solution of linear integral equations by Taylor ordering method: Applied mathematical approach

Since obtaining an analytic solution to some mathematical and physical problems is often very difficult, academics in recent years have focused their efforts on treating these problems using numerical methods. In science and engineering, systems of integral differential equations and their solutions...

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Bibliographic Details
Published in:	Open Physics Vol. 20; no. 1; pp. 850 - 858
Main Authors:	Ghamkhar, Madiha, Wajid, Laiba, Shahzad, Khurrem, Safdar, Rabia, Alhazmi, Sharifah E., Lashin, Maha M. A., Jamshed, Wasim, Eid, Mohamed R., Alkhatib, Soliman
Format:	Journal Article
Language:	English
Published:	De Gruyter 03-09-2022
Subjects:	collocation points system of integral differential equation Taylor polynomial Taylor series
Online Access:	Get full text
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Summary:	Since obtaining an analytic solution to some mathematical and physical problems is often very difficult, academics in recent years have focused their efforts on treating these problems using numerical methods. In science and engineering, systems of integral differential equations and their solutions are extremely important. The Taylor collocation method is described as a matrix approach for solving numerically Linear Differential Equations (LDE) by using truncated Taylor series. Integral equations are used to solve problems such as radiative transmission and the oscillation of a string, membrane, or axle. Differential equations can be used to tackle oscillating difficulties. To discover approximate solutions for linear systems of integral differential equations with variable coefficients in terms of Taylor polynomials, the collocation approach, which is offered for differential and integral equation solutions, will be developed. A system of LDE will be translated into matrix equations, and a new matrix equation will be generated in terms of the Taylor coefficients matrix by employing Taylor collocation points. The needed system will be converted to a linear algebraic equation system. Finding the Taylor coefficients will lead to the Taylor series technique.
ISSN:	2391-5471 2391-5471
DOI:	10.1515/phys-2022-0182