Author : Suresh Arjula 1
Date of Publication :21st February 2018
Abstract: The present work involves in the use the NURBS basis functions, with varying degree, as the basis functions in Collocation Method. A comprehensive step-by-step procedure for using NURBS Collocation method is developed and documented for applying this method to heat transfer problems. This method is applied to 1-D conductive Heat Transfer through the slab. The results obtained with NURBS Collocation Method are closed to the exact solution. The solution obtained by collocation method is found to be accurate and far simpler to solve than many available approximate methods.
- J.N.Reddy, “An Introduction to the Finite Element Method”, 3rd ed., Tata McGraw-Hill Edition, New Delhi, 2005.
- Ch. Sridhar Reddy, Y. Rajashekhar Reddy and P. Srikanth, “Application of B-spline Finite Element Method for One Dimensional Problems”, International Journal of Current Engineering and Technology, April2014.
- Hughes, T.J.R., Cottrell, J.A. and Bazilevs, Y. „„Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement‟‟, Comput. Methods Appl. Mech. Engg., 194(39–41), pp. 4135– 4195 (2005).
- Sharanjeet Dhawan And Sheo Kumar, "A Galerkin BSpline Approach to One Dimensional Heat Equation", International Journal of Research and Reviews in Applied Sciences, Volume 1, Issue 1, 2009.
- Samuel Jator and Zachariah Sinkala. “A high order Bspline collocation method for linear boundary value problems” Eslevier, Applied Mathematics and Computation 191 (2007) 100–116.
- O.Botlla, “On a collocation B-spline method for the solution of the Navier–Stokes equations”, Pergamon, Computers & Fluids 31 (2002), p. 397–420.
- Bharti Gupta and V.K. Kukreja, “Numerical approach for solving diffusion problems using cubic B-spline collocation method” Eslevier, Applied Mathematics and Computation Vol. 219, 2012, p. 2087–2099
- K.N.S. Kasi Viswanadham and Y. Showri Raju, "Quartic B-Spline Collocation Method for Fifth Order Boundary Value Problems", International Journal of Computer Applications (0975–8887) Volume 43– No.13, April 2012.
- V.Dabral, S.Kapoor and S.Dhawan, " Numerical Simulation of one dimensional Heat Equation: BSpline Finite Element Method", Indian Journal of Computer Science and Engineering (IJCSE). Vol.2 No.2, 2011.
- David F. Rogers and J. Alan Adams, “Mathematical Elements for Computer Graphics”, 2nd ed., Tata McGraw-Hill Edition, New Delhi, 2002.