HIGHER-ORDER METHOD FOR SOLVING FREE BOUNDARY-VALUE PROBLEMS

REFERENCES

• Stewartson , K. 1964 . The Theory of Laminar Boundary Layers in Compressible Fluids , Oxford, UK : Oxford University Press .
   Google Scholar
• Smith , A. M. O. 1954 . Improved Solutions of the Falkner and Skan Boundary-Layer Equation, Fund Paper . J. Aero. Sci. , Fairchild, S.M., Inst. Aeronaut. Sci. Fund paper FF-10
   Google Scholar
• Cebeci , T. and Keller , H. B. 1971 . Shooting and Parallel Shooting Methods for Solving the Falkner-Skan Boundary-Layer Equation . J. Comput. Phys. , 7 : 289 – 300 .
   Web of Science ®Google Scholar
• Na , T. Y. 1979 . Computational Methods in Engineering Boundary Value Problems , New York : Academic Press .
   Google Scholar
• Rosenhead , L. 1963 . Laminar Boundary Layers , 107 – 125 . Oxford, UK : Oxford University Press .
   Google Scholar
• White , F. M. 1991 . Viscous Fluid Flow , 2d ed. , 243 – 247 . McGraw-Hill . 2nd ed., pp. 243-247, New York
   Google Scholar
• Fazio , R. and Similarity , A . 1998 . Approach to the Numerical Solution of Free Boundary Problems . SIAM Rev. , 40 : 616 – 635 .
   Web of Science ®Google Scholar
• Fazio , R. 2002 . A Survey on Free Boundary Identification of the Truncated Boundary in Numerical BVPs on Infinite Intervals . J. Comput. Appl. Math. , 140 : 331 – 344 .
   Web of Science ®Google Scholar
• Asaithambi , A. 1998 . A Finite-Difference Method for the Falkner-Skan Equation . Appl. Math. Comput. , 92 : 135 – 141 .
   Web of Science ®Google Scholar
• Zaturska , M. B. , Banks , W. H. H. and New , A . 2001 . Solution Branch of the Falkner-Skan Equation . Acta Mech. , 152 : 197 – 201 .
   Web of Science ®Google Scholar
• Scavo , R. J. and Thoo , J. B. 1995 . On the Geometry of Halley's Method . Am. Math. Monthly , 102 : 417 – 426 .
   Web of Science ®Google Scholar
• Gutiérrez , J. M. and Hernández , M. A. 1997 . A Family of Chebyshev-Halley Type Methods in Banach Spaces . Bull. Austr. Math. Soc. , 55 : 113 – 130 .
   Web of Science ®Google Scholar
• Gutiérrez , J. M. , Hernández , M. A. and Salanova , M. A. 2001 . Calculus of nth order iterative methods . Nonlinear Anal. , 47 : 2875 – 2880 .
   Web of Science ®Google Scholar
• Lambert , J. D. 1973 . Computational Methods in Ordinary Differential Equations , London, UK : Wiley .
   Google Scholar
• Usmani , R. A. and Agarwal , R. P. 1985 . An A-Stable Extended Trapezoidal Rule for the Numerical Integration of Ordinary Differential Equations . Comput. Math. Appl. , 11 : 1183 – 1191 .
   Web of Science ®Google Scholar
• Jacques , I. B. 1989 . Extended One-Step Methods for the Numerical Solution of Ordinary Differential Equations . Int. J. Comput. Math. , 29 : 247 – 255 .
   Web of Science ®Google Scholar
• Kondrat , D. M. and Jacques , I. B. 1992 . Extended A-Stable Two-Step Methods for the Numerical Solution of Ordinary Differential Equations . Int. J. Comput. Math. , 42 : 117 – 124 .
   Web of Science ®Google Scholar
• Chawla , M. M. , Al-Zanaidi , M. A. and Al-Sahhar , M. S. 1994 . Stabilized Fourth Order Extended Methods for the Numerical Solution of ODEs . Int. J. Comput. Math. , 52 : 99 – 107 .
   Web of Science ®Google Scholar
• Chawla , M. M. , Al-Zanaidi , M. A. and Al-Sahhar , M. S. 1995 . A Class of Stabilized One-Step Methods for the Numerical Solution of ODEs . Comput. Math. Appl. , 29 : 79 – 84 .
   Web of Science ®Google Scholar
• Chawla , M. M. , Al-Zanaidi , M. A. and Evans , D. J. 1996 . A Class of Generalized Trapezoidal Formulas for the Numerical Integration of y′ = f(x, y) . Int. J. Comput. Math. , 62 : 131 – 142 .
   Web of Science ®Google Scholar
• Van Hecke , T. , Vanden Berghe , G. , Van Daele , M. and De Meyer , H. 1997 . A Variable-Step Variable-Order Algorithm for Systems of Stiff ODEs . Int. J. Comput. Math. , 63 : 149 – 157 .
   Web of Science ®Google Scholar
• Lambert , J. D. 1991 . Numerical Methods for Ordinary Differential Systems , London, UK : Wiley .
   Google Scholar
• Wadia , A. R. and Payne , F. R. 1981 . A Boundary Value Technique for the Analysis of Laminar Boundary Layer Flows . Int. J. Comput. Math. , 9 : 163 – 172 .
   Web of Science ®Google Scholar
• Beckett , P. M. 1983 . Finite Difference Solution of Boundary-Layer Type Equation . Int. J. Comput. Math. , 14 : 183 – 190 .
   Web of Science ®Google Scholar
• Fazio , R. 1996 . A Novel Approach to the Numerical Solution of Boundary Value Problems on Infinite Intervals . SIAM J. Numer. Anal. , 33 : 1473 – 1483 .
   Web of Science ®Google Scholar
• Schlichting , H. and Gersten , K. 1960 . Boundary Layers Theory , 4th ed. , 142 – 175 . New York : Springer-Verlag .
   Google Scholar
• Fazio , R. 1992 . The Blasius Problem Formulated as a Free Boundary Value Problem . Acta Mech. , 95 : 1 – 7 .
   Web of Science ®Google Scholar