Stable discrete solution of coupled singular mixed partial differential problems

References

• Argawal , R. P. 1992 . “ Difference Equations and Inequalities ” . In Theory, Methods and Applications , Dekker .
   Google Scholar
• Camacho , J. , Ferrer , M. V. and Navarro , E. 1997 . Analytic-numerical solutions with a prefixed accuracy for partial differential systems with coupled separated boundary value conditions . Appl Sci. Compt. , 4 ( 2 ) : 104 – 116 .
   Google Scholar
• Camacho , J. , Jódar , L. and Navarro , E. 1998 . Exact solution of coupled mixed diffusion problems with coupled boundary conditions . Mathl. Comput. Modelling , 28 : 65 – 76 .
   Web of Science ®Google Scholar
• Campbell , S. L. and Meyer , C. D. Jr. 1979 . Generalized Inverses of Linear Transformations , London : Pitman .
   Google Scholar
• Cannon , J. R. and Klein , R. E. 1973 . On the observability and stability of the temperature distribution in a composite heat conductor . SIAM J. Appl. Math. , 24 : 596 – 602 .
   Web of Science ®Google Scholar
• Chiu , H. H. 1969 . Theory of irreductible linear systems . Quart. Appl. Math. , XXVII : 87 – 104 .
   Google Scholar
• Courant , R. and Hilbert , D. 1962 . Methods of Mathematical Physics , Vol. II , New York : Interscience .
   Google Scholar
• Dunford , N. and Schwartz , J. 1957 . “ Part I ” . In Linear Operators , New York : Interscience .
   Google Scholar
• Golub , G. H. and Van Loan , C. F. 1989 . Matrix Computations , Baltimore , MA : Johns Hopkins Univ. Press .
   Google Scholar
• Hodgkin , A. L. and Huxley , A. F. 1952 . A quantitative description of membrane current and its applications to conduction in the giant axon of Loligo . J. Physiol. , 117 : 500 – 544 .
   PubMed Web of Science ®Google Scholar
• Jódar , L. and Legua , M. 1991 . Resolutión numerica de sistemas acoplados de ecuaciones en derivadas parciales . Rev. Int. Métodos Numer. Cálculo y Dis. en Ing. , 7 ( 3 ) : 289 – 299 .
   Google Scholar
• Jódar , L. , Sánchez , J. A. and Ferrer , M. V. 2000 . The Stable Discrete Numerical Solution of Strongly Coupled Mixed Partial Differential Systems . Computers and Mathematics with Applications , 39 : 169 – 182 .
   Web of Science ®Google Scholar
• Jódar , L. and Sánchez , J. A. 1999 . Constructive Stable Numerical Solutions for Strongly Coupled Diffusion Mixed partial Differential Systems . Int. J. Computers and Math. , 73 ( 2 )
   Google Scholar
• Kee R. J. Petzold L. R. A differential/algebraic equation formulation of the method- of-lines solution to systems of partial differential equations Technical Report SAND86- 8893 Sandia National Laboratories 1986
   Google Scholar
• Legua , M. , Jódar , L. and Law , A. G. 1992 . “ Existence of numerical solutions for singular partial differential systems ” . In Iterative Methods in Linear Algebra , Edited by: Beauwens , R. and De Groen , P. 395 – 400 . Elsevier .
   Google Scholar
• Magcagni , M. 1989 . An initial-boundary value problem of physiological significance for equations of nerve conduction . Communications on Pure and Applied Mathematics , XLII : 213 – 227 .
   Google Scholar
• Mirsky , L. 1990 . An Introduction to Linear Algebra , New York : Dover .
   Google Scholar
• Ortega , J. M. 1972 . Numerical Analysis, A Second Course , New York : Academic Press .
   Google Scholar
• Ösizik , M. N. 1994 . Finite Difference Methods in Heat Transfer , London : CRC Press .
   Google Scholar
• Rao , C. R. and Mitra , S. K. 1971 . Generalized Inverse of Matrices and its Applications , New York : John-Wiley .
   Google Scholar
• Sezgin , M. 1987 . Magnetohydrodynamic flow in a rectangular duct . Int. J. Numer. Methods Fluids , 7 : 686 – 718 .
   Google Scholar
• Sheng , D. and Axelsson , K. 1995 . Uncoupling of coupled flows in soil - A finite element method . Int. J. for Numerical and Analytical Methods in Geomechanics , 19 : 537 – 553 .
   Web of Science ®Google Scholar
• Smith , G. D. 1978 . Numerical Solution of Partial Differential equation: Difference Methods , Oxford : Clarendon Press .
   Google Scholar
• Villanueva , R. J. , Hervás , A. and Salazar , M. J. 1999 . Analytical-Numerical Solution of Coupled Singular Mixed Diffusion Type Problems . Mathematical and Computer Modelling , 38 : 93 – 106 .
   Google Scholar
• Winfree , A. T. 1997 . Heart Muscle as a Reaction-Diffusion Medium: The Roles of Electric Potential Diffusion. Activation Front Curvature, and Anisotropy . Int. J. Bif Chaos , 7 March : 487 – 526 .
   Web of Science ®Google Scholar
• Winfree , A. T. 1998 . A Spatial Scale Factor for Electrophysiological Models of Myocardium . Prog. Biophys. Molec. Biol , 69 March : 185 – 203 .
   PubMed Web of Science ®Google Scholar
• Wolfram , S. 1996 . The Mathematica book , Wolfram Media Inc .
   Google Scholar