On the Convergence of a Spline Method for Singular Two Point Boundary Value Problems Arising in Physiology

References

• Adam , J. A. 1986 . A simplified mathematical model of tumor growth . Math. Biosci. , 81 : 224 – 229 .
   Web of Science ®Google Scholar
• Adam , J. A. 1987 . A mathematical model of tumor growth II: Effect of geometry and spatial nonuniformity on stability . Math. Biosci. , 86 : 183 – 211 .
   Web of Science ®Google Scholar
• Adam , J. A. 1987 . A mathematical model of tumor growth III: Comparison with experiment . Math. Biosci. , 86 : 313 – 227 .
   Web of Science ®Google Scholar
• Adam , J. A. and Maggelakis , S. A. 1989 . Mathematical model of tumor growth IV: Effect of necrotic core . Math. Biosci. , 97 : 121 – 136 .
   PubMed Web of Science ®Google Scholar
• Burton , A. C. 1966 . Rate of growth of solid tumor as a problem of diffusion . Growth , 30 : 157 – 176 .
   PubMedGoogle Scholar
• Chawla , M. M. and Katti , C. P. 1982 . Finite difference methods for a class of singular two point boundary value problems . Numer. Math. , 39 : 341 – 350 .
   Web of Science ®Google Scholar
• Flesch , U. 1975 . The Distribution of heat sources in the human head: A theoretical consideration . J. Theor. Biol. , 54 : 285 – 287 .
   PubMed Web of Science ®Google Scholar
• Garner , J. B. and Shivaji , R. 1990 . Diffusion problems with mixed nonlinear boundary condition . J. Math. Anal. Applic. , 148 : 422 – 430 .
   Web of Science ®Google Scholar
• Gray , B. F. 1980 . The Distribution of heat sources in the human head: A theoretical consideration . J. Theor. Biol. , 82 : 473 – 476 .
   PubMed Web of Science ®Google Scholar
• Greenspan , H. P. 1972 . Models for the growth of solid tumor by diffusion . Studies Appl. Math. , 52 : 317 – 340 .
   Google Scholar
• Iyengar , S. R. K. and Jain , Pragya . 1987 . Spline finite difference methods for singular two point boundary value problems . Numer. Math. , 50 : 363 – 376 .
   Web of Science ®Google Scholar
• Lin , H. S. 1976 . Oxygen diffusion in a spherical cell with nonlinear oxygen uptake Kinetics . J. Theor. Biol. , 60 : 449 – 457 .
   PubMed Web of Science ®Google Scholar
• Massaro , T. A. and Fatt , I. 1969 . Oxygen diffusion in a large single-cell organisms . Bull. Math. Biophys. , 31 : 327 – 340 .
   PubMedGoogle Scholar
• McElwain , D. L. S. 1978 . A re-examination of oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake Kinetics . J. Theor. Biol. , 71 : 255 – 263 .
   PubMed Web of Science ®Google Scholar
• Pandey , R. K. 1996 . On a class of weakly regular singular two-point boundary value problems . II, J. Diff. Eq. , 127 (1} ) : 110 – 123 .
   Web of Science ®Google Scholar
• Pandey , R. K. 1997 . A finite difference methods for a class of singular two point boundary value problems arising in physiology . Inter. J. Comput. Math. , 65 : 131 – 140 .
   Web of Science ®Google Scholar
• Rashevsky , N. Mathematical Biophysics , Vol. I , New York : Dover, 1960 .
   Google Scholar