- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Advances in Mathematical Physics
Volume 2013 (2013), Article ID 350810, 6 pages
On New High Order Quasilinearization Approaches to the Nonlinear Model of Catalytic Reaction in a Flat Particle
1School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa
2Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha 7395, South Africa
3Department of Mathematics & Applied Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa
Received 28 September 2013; Accepted 8 November 2013
Academic Editor: Raseelo Joel Moitsheki
Copyright © 2013 S. S. Motsa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. Kierzenka and L. F. Shampine, “A BVP solver based on residual control and the MATLAB PSE,” ACM Transactions on Mathematical Software, vol. 27, no. 3, pp. 299–316, 2001.
- G. Damkohler, “Ubertemperatur in kontaktkornern. (Excess temperature in catalyst grains.),” Zeitschrift für Physikalische Chemie, vol. 193, pp. 16–28, 1943.
- D. N. Kim and Y. G. Kim, “An experimental study of multiple steady states in a porous catalyst due to phase transition,” Journal of Chemical Engineering of Japan, vol. 14, pp. 311–317, 1981.
- D. H. Kim and Y. G. Kim, “Simulation of multiple steady states in a porous catalyst due to phase transition,” Journal of Chemical Engineering of Japan, vol. 14, no. 4, pp. 318–322, 1981.
- D. N. Jaguste and S. K. Bhatia, “Partial internal wetting of catalyst particles: hysteresis effects,” AIChE Journal, vol. 37, pp. 650–660, 1991.
- O. D. Makinde, “Exothermic explosions in a Slab: a case study of series summation technique,” International Communications in Heat and Mass Transfer, vol. 31, no. 8, pp. 1227–1231, 2004.
- O. D. Makinde, “Strong exothermic explosions in a cylindrical pipe: a case study of series summation technique,” Mechanics Research Communications, vol. 32, pp. 191–195, 2005.
- L. D. Landau and Y. M. Lifshits, Statistical Physics, Nauka, Moscow, Russia, 1964, (Russian).
- V. Hlavácek, M. Marek, and M. Kubícek, “Modelling of chemical reactors, X: multiple solutions of enthalpy and mass balances for a catalytic reaction within a porous catalyst particle,” Chemical Engineering Science, vol. 23, pp. 1083–1097, 1968.
- C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods in Fluid Dynamics, Springer, Berlin, Germany, 1988.
- D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, Philadelphia, Pa, USA, 1977.
- L. N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, Pa, USA, 2000.
- R. E. Bellman and R. E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems, Elsevier, New York, NY, USA, 1965.
- J. Kierzenka and L. Shampine, “A BVP solver based on residual control and the Matlab PSE,” ACM Transactions on Mathematical Software, vol. 27, pp. 299–316, 2001.
- L. F. Shampine, I. Gladwell, and S. Thompson, Solving ODEs with MATLAB, Cambridge University Press, Cambridge, UK, 2003.
- Y. Lin, J. A. Enszer, and M. A. Stadtherr, “Enclosing all solutions of two-point boundary value problems for ODEs,” Computers & Chemical Engineering, vol. 32, pp. 1714–1725, 2008.