Green's Function and Its Applications
Keywords:
Green's function, Diffusion equation, Poisson's equations, Schrödinger equation, Laplace's equationsAbstract
In this research, we studied the concept of Green's function and its use in solving differential equations. In this study, we highlight some applications of Green's functions in applied sciences to emphasize their importance, as they significantly contribute to simplifying the process of finding precise and clear solutions to problems, particularly in boundary value and initial value problems, the wave equation, the diffusion equation, as well as Laplace's and Poisson's equations.
Downloads
References
[1]. Roach, G. 1982. Green's function. Cambridge.
[2]. Duffy, D. 2015. Green's Functions with Applications. CAC Press.
[3]. Carrier, G. Pearson, G. 1976. Partial Differential Equations. New York.
[4]. [4] Olver, P. 2014. Introduction to Partial Differentia Equations. Springer Cham Heidelberg, New York
[5]. Stakgold, I. Holst, M. 2011. Green's Functions and Boundary value problems. John wiley and sons Hobokon.
[6]. Panakhor, E. Yilmazer, R. 2011. On the Determination of the Hydrogen Atom Equation from Two Spectra. World Applied Sciences Journal 13 (10):2203 – 2210.
[7]. Taylor, M. 2006. Wave Equations and Diffraction. In Elsevier Encyclopedie of Mathematical Physics.
[8]. Howe, M. 2003 .Theory of Vortex Sound. Cambridge Texts in Applied Mathematics.
[9]. Linear, B. 2000. Partial Differential Equations for Scientists and Engineers. Boston Basel Berlin.
[10]. Asmar, N. 2004. Partial Differential Equations with Fourier Series and Boundary Value Problems. Prentice Hall . New Jersey.