Numerical methods for nonlinear fourth-order boundary value problems with applications

References

• Usmani , R. A. 1978 . Discrete variable methods for a boundary value problem with engineering applications . Mathematics of Computation , 32 : 1087 – 1096 .
   Google Scholar
• Ma , T. F. 2001 . Boundary stabilization for a non-linear beam on elastic bearings . Mathematical Methods in Applied Science , 24 : 583 – 594 .
   Web of Science ®Google Scholar
• Chandrasekhar , S. 1981 . Hydrodynamic and Hydromagnetic Stability , New York : Dover .
   Google Scholar
• Djidjeli , K. , Twizell , E. H. and Boutayeb , A. 1993 . Numerical methods for special nonlinear boundary-value problems of order 2m . Journal of Computational and Applied Mathrmatics , 47 : 35 – 45 .
   Web of Science ®Google Scholar
• Al-Khaled , K. and Naim Anwar , M. 2007 . Numerical comparison of methods for solving second-order ordinary initial value problems . Applied Mathematical Modelling , 31 : 292 – 301 .
   Web of Science ®Google Scholar
• Al-Said , E. A. and Noor , M. A. 2002 . Quartic spline method for solving fourth order obstacle boundary value problems . Journal of Computational and Applied Mathematics , 143 : 107 – 116 .
   Web of Science ®Google Scholar
• Jiang , D. , Liu , H. and Xu , X. 2005 . Nonresonant singular fourth-order boundary value problems . Applied Mathematics Letter , 18 : 69 – 75 .
   Google Scholar
• Pang , C. , Dong , W. and Wei , Z. 2006 . Multiple solutions for fourth-order boundary value problem . Journal of Mathematical Analysis and Applications , 314 : 464 – 476 .
   Google Scholar
• Agarwal , R. P. 1986 . Boundary Value Problems for High Ordinary Differential Equations , Singapore : World Scientific .
   Google Scholar
• Smith , R. C. , Bogar , G. A. , Bowers , K. L. and Lund , J. 1991 . The sinc–Galerkin method for fourth-order differential equations . SIAM Journal on Numerical Analysis , 28 : 760 – 788 .
   Web of Science ®Google Scholar
• Lund , J. and Bowers , K. L. 1992 . Sinc Methods for Quadrature and Differential Equations , Philadelphia : SIAM .
   Google Scholar
• Stenger , F. 1993 . Numerical Methods Based on Sinc and Analytic Functions , New York : Springer-Verlag .
   Google Scholar
• Wazwaz , A. M. 2000 . Approximate solution to boundary value problems of higher order by the modified decomposition method . Computers and Mathematics with Applications , 40 : 679 – 691 .
   Web of Science ®Google Scholar
• Cherrualt , Y. 1989 . Convergence of Adomian's method . Kybernetes , 18 : 31 – 38 .
   Web of Science ®Google Scholar
• Cherrualt , Y. and Adomian , G. 1993 . Decomposition methods: a new proof of convergence . Mathematical and Computer Modelling , 18 : 103 – 106 .
   Google Scholar
• Wazwaz , A. M. 1998 . A comparison between Adomain decomposition method and Taylor series method in the series solutions . Applied Mathematics and Computation , 79 : 37 – 44 .
   Web of Science ®Google Scholar
• He , J.-H. 1999 . Variational iteration method – A kind of non-linear analytical technique: some examples . International Journal of Non-Linear Mechanics , 34 : 699 – 708 .
   Web of Science ®Google Scholar
• El-Gamel , M. , Behiry , S. H. and Hashish , H. 2003 . Numerical method for the solution of special nonlinear fourth-order boundary value problems . Applied Mathematics and Computation , 145 : 717 – 734 .
   Web of Science ®Google Scholar
• Adomian , G. 1988 . A review of the decomposition method in applied mathematics . Journal of Mathematical Analysis and Applicatins , 135 : 501 – 544 .
   Web of Science ®Google Scholar
• Adomian , G. 1994 . Solving Frontier Problems of Physics: The Decomposition Method , Boston : Kluwer Academic Publishers .
   Google Scholar
• Khuri , S. A. 2004 . A new approach to Btatu's problem . Applied Mathematics and Computation , 147 : 131 – 136 .
   Web of Science ®Google Scholar
• Wazwaz , A. M. 2002 . The numerical solution of special fourth-order boundary value problems by the modified decomposition method . International Journal of Computer Mathematics , 79 : 345 – 356 .
   Web of Science ®Google Scholar
• Agarwal , R. P. and Akrivis , C. 1982 . Boundary value problems occurring in plate deflection theory . Journal of Computational and Applied Mathematics , 8 : 145 – 154 .
   Google Scholar
• Rashidinia , J. and Golbabaee , A. Convergence of numerical solution of a fourth-order boundary value problems . Applied Mathematics and Computation , 171 1296 – 1305 .
   Google Scholar