A new general polynomial transforms for solving ordinary differential equations with variable coefficients

Kuffi, Emad A.; Maktoof, Sara Falih

doi:10.22075/ijnaa.2021.6090

A new general polynomial transforms for solving ordinary differential equations with variable coefficients

Document Type : Research Paper

Authors

Emad A. Kuffi ¹

Sara Falih Maktoof ²

¹ Department of Materials Engineering, College of Engineering, Al-Qadisiyah University, Iraq

² Department of Mathematics, Faculty for Girls, University of Kufa, Iraq

10.22075/ijnaa.2021.6090

Abstract

In this paper, we introduce the definition of a new general integral transform which call it "A new general polynomial transform ". Also, we introduce properties, theorems, proofs and transforms of the Logarithmic functions, polynomials functions and other functions. As well as, we discuss how we can apply this integral transform and its inverse to solve the ordinary differential equations with variable coefficients.

Keywords

Integral transforms

Inverse integral transforms

Polynomial transform

Inverse polynomial transform

[1] K.S. Aboodh, The new integral transform , ”Aboodh transform”, Glob. Pure Appl. Math. 9(1) (2013).
[2] B. Barnes, Polynomail integral transform for solving differential equations, Eur. J. Pure Appl. Math. 9(2) (2016)
140–151.
[3] M. Braun, Differential Equation and Their Application, 4th Ed., New York, Spring-Verlag, 1993.
[4] Z.H. Khan and W.A. Khan, Natural transform-properties and applications, Nust J. Eng. Sci. 1 (2008).
[5] E.A. Mansour, S.A. Mehdi and E.A. Kuffi, The new integral transform and its applications, Int. J. Nonlinear
Anal. Appl. 12(2) (2021) 849–856.
[6] A.H. Mohmmed and A.N. Kathem, Solving Euler’s equation by using new transformation, J. Kerbala Univ. 6(4)
(2008) 103–109.
[7] G.K. Watugula, Sumudu transform: a new integral transform to solve differential equations and control engineering problems, Int. J. Math. Edn. Sci. Techol. 24(1) (1993) 35–43.
[8] T.M. Zaki, The new integral transform, ”Elzaki transform”, Glob. J. Pure . Appl. Math. 7(1) (2011) 57–64