On the Use of Green's Functions in Solving Boundary Value Problems

  • Aymaan S. Aboukhisheem Head of Department of Mathematics, Ghasr ben Ghisheer, Libya
  • Alham M. Al-Refai Department of Mathematics, University of Tripoli, Tripoli, Libya
  • Ahlam E. Elashegh Department of Mathematics, University of Tripoli, Tripoli, Libya
  • Ali M. Awin Department of Mathematics, University of Tripoli, Tripoli, Libya
Keywords: Green's Functions, Boundary Value Problems, Discrete ,Domain


There is no doubt that Green's functions have a long history in their use in many fields of applied mathematics and physics and especially in solving boundary value problems, hence we thought that it is worthwhile to write this article to summarize some important results in this concern emphasizing the beauty behind using them and the elegant mathematical techniques used as tools in conjunction with them. Famous problems relate to wave propagation and potential theory will be tackled in some details, giving the solutions of the partial differential equation which are connected with the problem. There remains also to
mention that Green's functions are used in many other applications as will be pointed out in the conclusions.


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[1] Aboukhisheem A.S.(2003) Green's Function and its Apllications,MSc.thesis,University of Tripoli, Tripoli,Libya.
[2] Arfken,G.(1970) Mathematical Methods for Physicists,2nd Edition, Academic Press,New York.
[3] Ivar,S.T.(1967) Boundary Value Problems ,1st Edition ,McMillan Company ,New York.
[4] Al-Refai,A.M.(2017) Discrete Green's Function, Master Thesis,Near East University, Nicosia.
[5] Pipes,L.A,Harvill,L.R.(1970) Applied Mathematics for Engineers and Physicists,3rd Edition,McGraw-Hill Book Company,Tokyo.
[6] Wang,W-X. (1991), The potential for a homogeneous cylinder in a cylindrical coordinate system, Quarterly of Applied Mathematics, XLIX,1,163-171
[7] Jackson,J.D.(1975) Classical Electrodynamics,2nd Edition,John Wiley and Sons,New York.
[8] Nafari,N.,Awin,A.M.(1992) The Calculation of Madelung Constant for NaCl Using the Method of Images, Physica Status Solidia,104,k21-k25.
[9] Dettman,J.W.(1962) Mathematical [9] Dettman,J.W.(1962) Mathematical Methods in Physics and Engineering,2nd Edition,McGraw –Hill Book
Company,New York.
[10] Husain,D,Suhrabuddib,S,Awin,A.M.(1985)Scattering at the Positive Energy Bound States, Australian Journal of Physics,38,539-545.
[11] Awin,A.M.(1991) Positive Energy bound States,Fortschritte der Physik ,2,131-158.
[12] Fayyad,H.M.,Rihan,T.,Awin,A.M.(1996) Inversion Solution to HeavyIon Optical Model Potential at Intermediate Energies, Physical
Review C,53,2334-2340.
[13] Delkhosh,M.,Delkhosh,M.,Jamali,M.(2012) Green's Function and its Applications, Journal of Basic and Applied Scientific Research,2,9,88658876.
[14] Aleixo,R.,Capelas de Oliveira,E.(2008) Green's Function for the Lossy Wave Equation,Revista Grasileira de Ensino de Fisica,30,1,1302- 1_5.
[15] Cabada,A.,Cid,J.A.,Maquez-Villamavin,B.(2012) Computation of Green's Functions for Boundary Value Problems with Matematica,
Applied Mathematics and Computation,219,1919-1936.
[16] Han,X.,Huang,J.(2015) The Generalized Green's Function for Boundary Value Problems of Second Order Difference Equations,Journal
of Function Spaces,2015,201946,1-7. http://dx.doi.org/10.1155/2015/201946
[17] Alhussein,M.(2021) Existence of Positive Solutions for a Fourth Order Three-Point Boundary Value Problem with Sign-Changing Green's Function,Applied Mathematics,12,311-321. https://www.scirp.org/journal/am
How to Cite
Aboukhisheem, A. S., Al-Refai, A. M., Elashegh, A. E., & Awin, A. M. (2022). On the Use of Green’s Functions in Solving Boundary Value Problems. Journal of Progressive Research in Mathematics, 19(1), 54-72. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/2141