Study of Cubic B Spline Interpolation NAJMUDDIN AHMAD 1 and KHAN FARAH DEEBA 2 Department of Mathematics, Integral University, Kursi Road, Lucknow (India) Corresponding Author Email: najmuddinahmad33@gmail.com http://dx.doi.org/10.22147/jusps-A/310201 Acceptance Date 30th January, 2019, Online Publication Date 14th February, 2019 This is an open access article under the CC BY-NC-SA license (https://creativecommons.org/licenses/by-nc-sa/4.0) JOURNAL OF ULTRA SCIENTIST OF PHYSICAL SCIENCES An International Open Free Access Peer Reviewed Research Journal of Mathematics website:- www.ultrascientist.org JUSPS-A Vol. 31(2), 4-10 (2019). Periodicity-Monthly Section A Estd. 1989 (Print) (Online) Abstract In this study, we discuss the numerical solution of the wave equation subject to non-local conservation condition, using cubic trigonometric B-spline collocation method (CuTBSM). Consider a vibrating elastic string of length L which is located on the x-axis of the interval [0, L]. It is also clear from the examples that the approximate solution is very close to the exact solution. The technique requires smaller computational time than several other methods and the numerical results are found to be in good agreement with known solutions and with existing schemes in the literature. Key words: Cubic trigonometric B Spline Interpolation, collocation method, non-Newtonian fluid, non- classical diffusion equation. Subject Classification: 65D,65L,65M Introduction There are quite a number of phenomena in science and engineering which can be modeled by the use of hyperbolic partial differential equations subject to non-local conservation condition instead of traditional boundary conditions 1 and these arise in the study of chemical heterogeneity 2,3 , medical science, visco-elasticity, plasma physics 4 and thermo elasticity 5,6 . This type of problems also arises in non-local reactive transport in underground water flows in porous media, semi-conductor modeling, non-Newtonian fluid flows and radioactive nuclear decay in fluid flows 7 . The temperature distribution of air near the ground over time during calm clear nights is a good example of such models 8 . The analysis, development and implementation of numerical methods for the solution of such problems have received wide attention in the literature. One of the most interesting equation in physical phenomena is reaction-diffusion equation. Since the equationis a model equation used in biology, chemistry, metallurgy and combustion, both analytical and numerical