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80-97

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- Department of Physics, Federal University of Technology Owerri, P.M.B. 1526, Owerri, Imo State, Nigeria

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- Department of Physics, Imo State University, Owerri, Nigeria

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- Department of Mathematics, Federal University of Technology Owerri, P.M.B. 1526, Owerri, Imo State, Nigeria

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References

- [1] Tan, Arjun and Edwards, Matthew E. (2010). Electrostatics and Dimensions of space. Georgia Journal of Science, vol 68, No 2, Article, 8.
- [2] Piaggio, H. (1930). An Introduction to the Geometry of N Dimensions. Nature 125, pp 266-267. https://doi.org/10.1038/125266a0
- [3] Kendall Ma (1963). A course in the Geometry of n Dimensions. The Mathematical Gazette Vol. 47, No. 359. p. 76 (1 page). https://doi.org/10.2307/3612075
- [4] Manning, Henry. P. (1915). Geometry of Four Dimensions. Nature 95, pp 282-283. https://doi.org/10.1038/095282a0.
- [5] Wein O. (1926). Quantentheorie and Funfdimrnsionale relativitatstheories. Zeitschrift Fur Phys. A Hadrons and Nuclei 37: pp. 895-906
- [6] Matthias A. Onabid (2012). Solving three-dimensional (3D) Laplace equations by Successive over- relaxation methods. African Journal of Mathematics and Computer Science Research, Vol 5(13), pp. 204-208
- [7] Vemuri V. and Karplus W. (1981). Digital Computer Treatment of PDE. Prentice-Hall, Englewood Cliffs, N.J. PP. 17-35
- [8] Brandt A. Diskin B. (1999). Multigrid Solvers for nonaligned somic flows. SIAMJ. Sci. Comput. Vol 21(2), pp. 473-501
- [9] Li, Y.L., Liu, C. H and Franke, S. J. (1990). Three dimensional Green’s function for wave propagation in a linearly inhomogeneous medium- the exact analytic solution. The Joutnal of The Acoustical Society of America, 87, 2285-2291
- [10] Churchill, R. V. (1954). The Operational Calculus of Legendre Transforms. Journal of Mathematics and Physics, 33, 165-178
- [11] Kellogg, O. D. (1955). Foundations of Potential Theory. The Mathematical Gazette Vol. 39, No. 377, pp. 88 (1). https://doi.org/10.2307/3611139
- [12] Stephane Mottin (2015). An analytical solution of the Laplace equation with the Robin conditions by applying Legendre transform. Integral Transforms and Special Function Vol. 27. No. 4, pp. 289-306. https://doi.org/10.1080/10652469.2015.1121255
- [13] Morse, P. M. and Feshbach, H. (1956). Methods of Theoretical Physics. Bull. Amer. Math. Soc. Vol. 62, Issue no. 1, pp. 52-54
- [14] Hassan Ettayeb and Adem Kilicman (2008). Anose on solutions of wave, Laplace’s and heat equations with convolution terms by using a double Laplace transform. Applied Mathematics Latter, Vol 21(12), pp. 1324-1329
- [15] Tsugio Fukuchi (2019). High-order accurate and high-speed calculation system of 1D Laplace and Poisson equations using the interpolation finite difference method. AIP Advances 9, 055312; doi: 10.1063/1.5096395
- [16] Morro, A. (1996). Introductory applications of partial differential equations. Meccanica Vol. 31, pp.717-721. https://doi.org/10.1007/BF00426978
- [17] Whittaker, E. (1932). Partial Differential Equations of Mathematical Physics. Nature 129, pp. 850-851. https://doi.org/10.1038/129850a0
- [18] Christain Constanda (2003). Solution Techniques for Elementary Partial Differential Equations. Society for Industrial and Applied Mathematics. Vol. 45, Issue no. 2, pp. 379-380
- [19] Hassan Eltayeb, Adem Kılıçman. (2008). A note on solutions of wave, Laplace’s and heat equations with convolution terms by using a double Laplace transform. Applied Mathematics Letters Vol. 5(21), pp. 1324-1329
- [20] V. A. Ditkin, A. P. Prudnikov, D. M. G. Wishart, I. N. Sneddon, (1963). Operational Calculus in Two Variables and Its Applications. Physics Today 16, 1, 72. https://doi.org/10.1063/1.3050726
- [21] Ali Babakhani, R. S. Dahiya (2001). Systems of Multi-dimensional Laplace transform and heat equation. In 16th Conference on Applied Mathematics, Univ. of Central Oklahoma, Electronic Journal of Differential Equations Conf. 07; pp. 25-36.
- [22] Mathias A. Onabid. (2012). Solving three-dimensional (3D) Laplace equations by successive over-relaxation method. African Journal of Mathematics and Computer Science Research Vol. 5(13), pp. 204-208

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