Solution of inverse ODE using Bezier functions

References

• Cheney, M, 1997. Inverse boundary-value problems, Am. Sci. 85 (1997), pp. 448–455.
   Web of Science ®Google Scholar
• Martin, TJ, and Dulikravich, GS, 1996. Inverse determination of boundary conditions and sources in steady heat conduction with heat generation, J. Heat Transfer 118 (1996), pp. 546–554.
   Web of Science ®Google Scholar
• Shih-Yu, S, 1999. A numerical study of inverse heat conduction problems, Comput. Math. Appl. 38 (1999), pp. 173–188.
   Web of Science ®Google Scholar
• Kurt, B, and Caudill, LF, 1996. An inverse problem in thermal imaging, SIAM J. Appl. Math. 56 (1996), pp. 715–735.
   Web of Science ®Google Scholar
• G.S. Dulikravich, J.M. Thomas, and B.H. Dennis, Multidisciplinary Inverse Problems, Proceedings of the Inverse Problems in Engineering, Theory and Practice, 3rd International Conference on Inverse Problem in Engineering, WA, USA, June 13–18, 1999..
   Google Scholar
• P. Venkataraman, Inverse Airfoil Design using Design Optimization, Paper no. 96-2503, 14th AIAA Applied Aerodynamics Conference, New Orleans, LA, June 1996..
   Google Scholar
• B.H. Dennis, A Least-Squares Finite Element Formulation for Inverse Detection of Unknown Boundary Conditions in Steady Heat Conduction, DETC2008-49653, ASME 28th Computers and Information in Engineering Conference, Brooklyn, NY, 2008..
   Google Scholar
• Tadi, M, 2000. Evaluation of a two-dimensional conductivity function based on boundary measurements, J. Heat Transfer 122 (2000), pp. 367–371.
   Web of Science ®Google Scholar
• Martin, TJ, and Dulikravich, GS, 1998. Inverse determination of steady heat convection coefficient distributions, ASME J. Heat Transfer 120 (1998), pp. 328–334.
   Web of Science ®Google Scholar
• Loulou, T, 2007. Combined parameter and function estimation with applications to thermal conductivity, J. Heat Transfer 129 (2007), pp. 1309–1320.
   Web of Science ®Google Scholar
• Monde, M, and Mitsutake, Y, 2001. A new estimate of thermal diffusivity using analytical inverse solution for one-dimensional heat conduction, Int. J. Heat Mass Transfer 44 (2001), pp. 3169–3177.
   Web of Science ®Google Scholar
• A.M. Hernandez, G.S. Dulikravich, S. Blower, M.J. Colaco, and R.J. Moral, Identification of Parameters in a System of Differential Equations Modeling Evolution of Infectious Diseases, DETC2008-49595, 28th ASME Computers and Information in Engineering Conference, Brooklyn, NY, 2008..
   Google Scholar
• Woodfield, PL, Monde, M, and Mitsutake, Y, 2006. Improved analytical solution for inverse heat conduction problems on thermally thick and semi-infinite solids, Int. J. Heat Mass Transfer 49 (2006), pp. 2864–2876.
   Web of Science ®Google Scholar
• Dennis, BH, Dulikravich, GS, and Yoshimura, S, 2004. A finite element formulation for the determination of unknown boundary conditions for 3D steady thermoelastic problems, ASME J. Heat Transfer 126 (2004), pp. 110–118.
   Web of Science ®Google Scholar
• Wang, J, and Zabaras, N, 2004. A Bayesian inference approach to the inverse heat conduction problem, Int. J. Heat Mass Transfer 47 (2004), pp. 3927–3941.
   Web of Science ®Google Scholar
• Deng, S, and Hwang, Y, 2006. Applying neural networks to the solution of forward and inverse heat conduction problems, Int. J. Heat Mass Transfer 49 (2006), pp. 4732–4750.
   Web of Science ®Google Scholar
• P. Venkataraman, Explicit solutions for differential equation, Available at http://people.rit.edu/pnveme/ExplictSolutions2/index.html.
   Google Scholar
• P. Venkataraman, A New Class of Analytical Solutions to Nonlinear Boundary Value Problems, DETC2005-84604, 25th Computers and Information in Engineering (CIE) Conference, Long Beach, CA, September, 2005..
   Google Scholar
• P. Venkataraman and J.G. Michopoulos, Explicit Solutions for Nonlinear Partial Differential Equations using Bezier Functions, DETC2007-35439, 27th Computers and Information in Engineering (CIE) Conference, Las Vegas, NA, September, 2007..
   Google Scholar
• P. Venkataraman, One and Two Dimensional Data Handling using Bezier Functions, DETC2008-49101, 28th Computers and Information in Engineering (CIE) Conference, Brooklyn, NY, August, 2008..
   Google Scholar
• P. Bezier, How Renault uses numerical control for car body design and tooling, SAE Paper no. 680010, Society of Automotive Engineers’ Congress, Detroit, MI, 1968..
   Google Scholar
• Rogers, DF, and Adams, JA, 1990. Mathematical Elements for Computer Graphics, . London: McGraw-Hill; 1990.
   Google Scholar
• Gordon, WJ, and Riesenfeld, RF, 1974. Bernstein-Bezier methods for the computer-aided design of free form curves and surfaces, J. ACM 21 (2) (1974), pp. 293–310.
   Web of Science ®Google Scholar
• Venkataraman, P, 2009. Applied Optimization with MATLAB Programming, . New York: John Wiley; 2009.
   Google Scholar