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Original Articles

Numerical Solution of Singularly Perturbed Non-Linear Two Point Boundary Value Problems by Spline in Compression

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Pages 271-288 | Published online: 15 Sep 2010

References

  • Abrahamsson , L. and Osher , S. 1982 . Monotone Difference Schemes for Singular Perturbation Problems . SIAM J. Numer. Anal. , 19 : 979 – 992 .
  • Ardema , M. D. , ed. 1983 . Singular Perturbations in Systems and Control , New York : Springer-Verlag .
  • Ascher , U. and Weiss , R. 1984 . Collocation for Singular Perturbation Problems, III: Nonlinear Problems without Turning Points . SIAM J. Sci. Stat. Comput. , 5 : 811 – 829 .
  • Chang , K. W. and Howes , F. A. 1984 . Nonlinear Singular Perturbation Phenomena: Theory and Application , New York : Springer-Verlag .
  • Bellman , R. and Kalaba , R. 1965 . Quasilinearization and Nonlinear Boundary Value Problems , New York : American Elsevier .
  • Bender , C. M. and Qrszag , S. A. 1978 . Advanced Mathematical Methods for Scientists and Engineers , New York : McGraw-HILL .
  • Berger , A. E. , Solomon , J. M. and Ciment , M. 1981 . An Analysis of a Uniformly Accurate Difference Method for a Singular Perturbation Problem . Math. Camp. , 37 : 79 – 94 .
  • Blatov , I. A. , Blatova , V. V. , Rozhec , Y. B. and Strygin , V. V. 1997 . Galerkin-Petrov method for strongly nonlinear singularly perturbed boundary value problems on special meshes . Appl. Numer. Math. , 25 (4} ) : 321 – 332 .
  • Carrier , G. F. 1970 . Singular Perturbations and Geophysics . SIAM Rev. , 12 : 175 – 193 .
  • Cash , J. R. 1988 . On the numerical integration of nonlinear two point boundary value problems using iterated deferred corrections, II. The development and analysis of Highly stable deferred correction formulae . SIAM J. Numer. Anal. , 25 : 862 – 882 .
  • Cash , J. R. and Wright , M. H. 1991 . A deferred correction method for nonlinear two point boundary value problems: implementation and numerical evaluation . SIAM J. Sci. Stat. Comput. , 12 : 971 – 989 .
  • Donald , L. Turcotte and Schubert , G. 1982 . Geodynamics: application of continuum physics to geological problems , Wiley .
  • Doolan , E. P. , Miller , J. J. H. and Schilders , W. H. A. 1980 . Uniform Numerical Methods For Problems With Initial And Boundary Layers , Dublin : Boole Press .
  • Hanks , T. C. 1971 . Model Relating Heat-Flow Values near and Verfiele Velocities of Mass Transport beneath Oceanic Rises . J. Geophys. Res. , 76 (2} ) : 537 – 544 .
  • Howes , F. A. 1976 . Singular Perturbations and Differential Inequalities . Memoirs of the AMS , : 168
  • Howes , F. A. 1978 . Boundary-Interior Layer Interactions in Nonlinear Singular Perturbation Theory , Memoirs of the American Mathematical Society, No. 203 Rhode Island : Providence .
  • Jain , M. K. 1979 . Spline Function Approximation in Discrete Mechanics . Int. J. Non-Linear Mechanics , 14 : 341 – 345 .
  • Kellogg , R. B. and Tsan , A. 1978 . Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points . Math. Comp. , 32 : 1025 – 1039 .
  • Kreiss , B. and Kreiss , H. O. 1981 . Numerical Methods for Singular Perturbation Problems . SIAM J. Numer. Anal. , 18 : 262 – 276 .
  • Maier , M. R. 1986 . An Adaptive Shooting Method for Singularly perturbed Boundary Value Problems . SIAM J. Sci. Stat. Comput. , 7 : 418 – 440 .
  • Marusic , M. and Rogina , M. 1996 . A Collocation Method for Singularly Perturbed Two-Point Boundary Value Problems with Spline in Tension . Advances in Computational Mathematics , 6 (1} ) : 65 – 76 .
  • Nayfeh , A. H. 1981 . Introduction to Perturbation Techniques , New York : John Wiley & Sons .
  • O'Malley , R. E. 1974 . Introductions to Singular Perturbations , New York : Academic Press .
  • Pearson , C. E. 1968 . On Non-Linear Ordinary Differential Equations of Boundary Layer Type . J. Math. and Phy. , 47 : 351 – 358 .
  • Ramos , J. I. and Garcia-Lopez , C. M. 1997 . Nonstandard finite difference equations for ODEs and 1-D PDEs based on piecewise linearization . Appl. Math. Comp. , 86 (1} ) : 11 – 36 .
  • Vulanovic , R. 1988 . High Order Monotone Schemes for a Nonlinear Singular Perturbation Problem . Z. Angew. Math. Mech. , 68 (5} ) : T428 – T430 .
  • Vulanovic , R. 1991 . A Second Order Numerical Method for Nonlinear Singular Perturbation Problems Without Turning Points . Akademiya-Nauk-SSSR.-Zhumal- Vychislitelnoi-Matematiki-i-Matematicheskoi-Fiziiki , 31 (4} ) : 522 – 532 .
  • Vulanovic , R. , Farrell , P. A. and Lin , P. 1993 . “ Numerical Solution of Nonlinear Singular Perturbation Problems Modelling Chemical Reactions ” . In Applications of Advanced Computational Methods for Boundary and Interior Layers , 192 – 213 . Dublin : Boole Press .
  • Wang , G. Y. 1994 . The application of integral equations to the numerical solution of nonlinear singular perturbation problems . J. Comp. Math. , 12 (1} ) : 36 – 45 .

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