Normal variables transformation method applied to free boundary value problemsFootnote^∗

^∗The present work was supported by the C.N.R. through contract no. 88.01855.01

References

• Ames , W.F. and Adams , E. 1976 . Exact shooting and eigenparameter problems . Nonlinear Anal Theory, Methods Appl , 1 : 75 – 82 .
   Google Scholar
• Bluman , G.W. and Cole , J.D. 1974 . Similarity Methods for Differential Equations , Berlin : Springer-Verlag .
   Google Scholar
• Cryer , C.W. 1971 . The method of Christopherson for solving free boundary problems for infinite journal bearings by means of finite differences . Math. Comput , 25 : 435 – 443 .
   Web of Science ®Google Scholar
• Dresner , L. 1983 . “ Similarity solutions of non-linear partial differential equations ” . In Research Notes in Math , Vol. 88 , Pitman .
   Google Scholar
• Epperson , J.F. 1986 . Analysis and implementation of an oxygen absorption model . SIAM Rev , 28 : 389 – 393 .
   Web of Science ®Google Scholar
• Fazio , R. 1990 . Numerical evaluations for shock and discontinuity velocity related to similarity solutions of quasilinear hyperbolic systems . J. Comput. Appl Maths , 30 : 341 – 349 .
   Google Scholar
• Fazio , R. 1990 . A noniterative transformation method applied to two-point boundary value problems . Appl Math. Comput , 30 to appear
   Google Scholar
• Fazio , R. and Evans , D.J. 1990 . Similarity and numerical analysis for free boundary value problems . Int. J. Comput. Math , 31 : 215 – 220 .
   Web of Science ®Google Scholar
• Fazio , R. 1990 . A nonlinear hyperbolic free boundary value problem . Acta Mech , 81 : 221 – 226 .
   Web of Science ®Google Scholar
• Hill , J.M. 1982 . “ Solution of differential equations by means of one-parameter groups ” . In Research Notes in Math , Vol. 63 , Pitman .
   Google Scholar
• Fortran Subroutines for Mathematical Applications 1989 IMSL MATH/LIBRARY, User's Manual, Version 1.1
   Google Scholar
• Meyer , G.H. 1973 . Initial Value Methods for Boundary Value Problems: Theory and Application of Invariant Imbedding , New York : Academic Press .
   Google Scholar
• Na , T.Y. 1967 . Transforming boundary conditions to initial conditions for ordinary differential equations . SIAM Rev , 9 : 204 – 210 .
   Web of Science ®Google Scholar
• Na , T.Y. 1979 . Computational Methods in Engineering Boundary Value Problems , New York : Academic Press .
   Google Scholar
• Rice , J.R. 1983 . Numerical Methods, Software and Applications , New York : McGraw-Hill .
   Google Scholar
• Vabishchevich , P.N. 1982 . On the solution of the free-boundary problem for elliptic equations . USSR Comput. Maths. Math. Phys , 22 : 89 – 98 .
   Google Scholar