References
- Beasley , C. 1981 . Finite Element Solution to Nonlinear Partial Differential Equations , Denton, Tx : University of North Texas . Ph.D. Thesis
- Brown , B. , Jais , M. and Knowles , I. 2005 . A variational approach to an elastic inverse problem . Inverse Problems , 21 : 1953 – 1973 .
- Courant , R. , Friedrichs , K. O. and Lewy , H. 1928 . Uber die Partiellen Differenzengleichungen der Mathematisches Physik . Math. Ann. , 100 : 32 – 74 .
- Garcia-Ripoll , J. , Konotop , V. , Malomed , B. and Perez-Garcia , V. 2003 . A quasi-local Gross–Pitaevskii equation for attractive Bose-Einstein condensates . Math. Comput. Simulation , 62 : 21 – 30 .
- Karatson , J. 2004 . Constructive Sobolev gradient preconditioning for semilinear elliptic systems . Electron. J. Differential Equations , 75 : 1 – 26 .
- Karatson , J. and Farago , I. 2005 . Preconditioning operators and Sobolev gradients for nonlinear elliptic problems . Comput. Math. Appl. , 50 : 1077 – 1092 .
- Karatson , J. and Loczi , L. 2005 . Sobolev gradient preconditioning for the electrostatic potential equation . Comput. Math. Appl. , 50 : 1093 – 1104 .
- Knowles , I. and Yan , A. 2004 . On the recovery of transport parameters in groundwater modelling . J. Comp. Appl. Math. , 171 : 277 – 290 .
- Mahavier , W. T. 1997 . A numerical method utilizing weighted Sobolev descent to solve singular differential equations . Nonlinear World , 4 : 435 – 455 .
- Moler , C. Stiff differential equations . Available online at: http://www.mathworks.com/company/newsletters/news_notes/clevescorner/may03_cleve.html (accessed 20 September 2005)
- Mujeeb , D. and Sial , S. Sobolev gradient for stiff flame-size ODE . Paper presented at LUMS International Conference on Mathematics . Lahore, Pakistan.
- Neuberger , J. W. 1997 . “ Sobolev Gradients and Differential Equations ” . In Springer Lecture Notes in Mathematics 1670 , New York : Springer-Verlag .
- O'Malley , R. E. 1991 . “ Singular Perturbation Methods for Ordinary Differential Equations ” . New York : Springer-Verlag .
- Richardson , W. B. 2000 . Steepest descent using smoothed gradients . Appl. Math. Comp. , 112 : 241 – 254 .
- Sial , S. 2005 . Sobolev gradient algorithm for minimum energy states of s-wave superconductors: finite element setting . Supercond. Sci. Technol. 18 , : 675 – 677 .
- Sial , S. , Neuberger , J. , Lookman , T. and Saxena , A. 2003 . Energy minimization using Sobolev gradients: application to phase separation and ordering . J. Comput. Phys. , 189 : 88 – 97 .
- Sial , S. , Neuberger , J. , Lookman , T. and Saxena , A. Energy minimization using Sobolev gradients finite element setting . Paper presented at the World Conference on 21st Century Mathematics . Lahore, Pakistan.