Differential quadrature method (DQM) for a class of singular two-point boundary value problems

References

• Bellman , R. , Kashef , B. G. and Casti , J. 1972 . Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations . J. Comput. Phys. , 10 : 40 – 52 .
   Web of Science ®Google Scholar
• Bert , C. W. and Malik , M. 1996 . Differential quadrature method in computational mechanics: a review . Appl. Mech. Rev. , 49 : 1 – 27 .
   Google Scholar
• Chawla , M. M. and Katti , C. P. 1982 . Finite difference methods and their convergence for a class of singular two point boundary value problems . Numer. Math. , 39 : 341 – 350 .
   Web of Science ®Google Scholar
• Chen , R. P. 2005 . One-dimensional non-linear consolidation of multi-layered soil by differential quadrature method . Comput. Geotech. , 32 : 358 – 369 .
   Web of Science ®Google Scholar
• Chen , W. Q. , Lv , C. F. and Bian , Z. G. 2004 . Free vibration analysis of generally laminated beams via state-space-based differential quadrature . Compos. Struct. , 64 : 417 – 425 .
   Google Scholar
• Choi , S. T. and Chou , Y. T. Proceedings of American Society of Mechanical Engineers International Computer in Engineering Conference . Atlanta, Georgia, U.S.A. Structural analysis by differential quadrature method using the modified weighting matrices ,
   Google Scholar
• El-Sayed , S. M. 1998 . Multi-integral methods for nonlinear boundary value problems . Int. J. Comput. Math. , 72 : 259 – 265 .
   Google Scholar
• Evans , D. J. 1999 . Iterative methods for solving non-linear two point boundary value problems . Int. J. Comput. Math. , 72 : 395 – 401 .
   Web of Science ®Google Scholar
• Evans , D. J. and Mohanty , R. K. 2002 . Alternating group explicit method for the numerical solution of non-linear singular two point boundary value problems using a fourth-order finite difference method . Int. J. Comput. Math. , 79 : 1121 – 1131 .
   Web of Science ®Google Scholar
• Inc , M. and Evans , D. J. 2003 . The decomposition method for solving of a class of singular two-point boundary value problems . Int. J. Comput. Math. , 80 : 869 – 882 .
   Web of Science ®Google Scholar
• Kumar , M. 2002 . A three point finite difference method for a class of singular two-point boundary value problems . J. Comput. Appl. Math. , 145 : 89 – 97 .
   Web of Science ®Google Scholar
• Kumar , M. and Aziz , T. 2004 . A non-uniform mesh finite difference method and its convergence for a class of singular two-point boundary value problems . Int. J. Comput. Math. , 81 : 1507 – 1512 .
   Web of Science ®Google Scholar
• Liew , K. M. , Huang , Y. Q. and Reddy , J. N. 2004 . Analysis of general shaped thin plates by the moving least-squares differential quadrature method . Finite Elem. Anal. Des. , 40 : 1453 – 1474 .
   Web of Science ®Google Scholar
• Liu , F. L. and Liew , K. M. 1999 . Differential quadrature element method: a new approach for free vibration analysis of polar Mindlin plates having discontinuities . Comput. Methods Appl. Mech. Eng. , 179 : 407 – 423 .
   Web of Science ®Google Scholar
• Mohanty , R. K. 2005 . A family of variable mesh methods for the estimates of (du/dr) and solution of non-linear singular two-point boundary value problems with singularity . J. Comput. Appl. Math. , 182 : 173 – 187 .
   Web of Science ®Google Scholar
• Mohanty , R. K. and Arora , U. 2006 . A TAGE iterative method for the solution of non-linear singular two point boundary value problems using a sixth order discretization . Appl. Math. Comput. , 180 : 538 – 548 .
   Web of Science ®Google Scholar
• Mohanty , R. K. and Evans , D. J. 2003 . A fourth order cubic spline alternating group explicit method for non-linear singular two point boundary value problems . Int. J. Comput. Math. , 80 : 479 – 492 .
   Web of Science ®Google Scholar
• Mohanty , R. K. and Khosla , N. 2005 . A third-order-accurate variable-mesh TAGE iterative method for the numerical solution of two-point non-linear singular boundary value problems . Int. J. Comput. Math. , 82 : 1261 – 1273 .
   Web of Science ®Google Scholar
• Mohanty , R. K. and Khosla , N. 2006 . Application of TAGE iterative algorithms to an efficient third order arithmetic average variable mesh discretization for two-point non-linear boundary value problems . Appl. Math. Comput. , 172 : 148 – 162 .
   Web of Science ®Google Scholar
• Mohanty , R. K. , Evans , D. J. and Khosla , N. 2005 . An non-uniform mesh cubic spline TAGE method for non-linear singular two-point boundary value problems . Int. J. Comput. Math. , 82 : 1125 – 1139 .
   Web of Science ®Google Scholar
• O'Mahoney , D. C. 2003 . A differential quadrature solution of the two-dimensional inverse heat conduction problem . Int. Comm. Heat Mass Transfer , 30 : 1061 – 1070 .
   Google Scholar
• Pandey , R. K. 1996 . On a class of weakly regular singular two point boundary value problems, I . Nonlinear Anal. Theory Methods Appl. , 27 : 1 – 12 .
   Google Scholar
• Pandey , R. K. 1996 . On a class of weakly regular singular two point boundary value problems, II . J. Diff. Equ. , 127 : 110 – 123 .
   Web of Science ®Google Scholar
• Pandey , R. K. 1997 . On a class of regular singular two point boundary value problems . J. Math. Anal. Appl. , 208 : 388 – 403 .
   Web of Science ®Google Scholar
• Pandey , R. K. 2002 . On the convergence of a spline method for singular two point boundary value problems arising in physiology . Int. J. Comput. Math. , 79 : 357 – 366 .
   Web of Science ®Google Scholar
• Pandey , R. K. and Singh , A. K. 2003 . On the convergence of finite difference method for general singular boundary value problems . Int. J. Comput. Math. , 80 : 1323 – 1331 .
   Web of Science ®Google Scholar
• Pandey , R. K. and Singh , A. K. 2004 . On the convergence of a finite difference method for a class of singular boundary value problems arising in physiology . J. Comput. Appl. Math. , 166 : 553 – 564 .
   Web of Science ®Google Scholar
• Qu , R. and Agarwal , R. P. 1997 . A collocation method for solving a class of singular nonlinear two-point boundary value problems . J. Comput. Appl. Math. , 83 : 147 – 163 .
   Web of Science ®Google Scholar
• Schreiber , R. 1980 . Finite element methods of high order accuracy for singular two-point boundary value problems with non-smooth solutions . SIAM J. Numer. Anal. , 17 : 547 – 566 .
   Web of Science ®Google Scholar
• Shu , C. 1991 . Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation , UK : University of Glasgow . Ph.D. thesis
   Google Scholar
• Shu , C. 2000 . Differential Quadrature and Its Application in Engineering , London : Springer-Verlag .
   Google Scholar
• Shu , C. and Richards , B. E. 1992 . Application of generalized differential quadrature to solve two-dimensional incompressible Navier–Stokes equations . Int. J. Numer. Methods Fluids , 15 : 791 – 798 .
   Web of Science ®Google Scholar
• Striz , A. G. , Chen , W. L. and Bert , C. W. 1994 . Static analysis of structures by quadratic element method (QEM) . Int. J. Solids Struct. , 31 : 2807 – 2818 .
   Web of Science ®Google Scholar
• Yücel , U. 2006 . Approximations of Sturm-Liouville eigenvalues using differential quadrature (DQ) method . J. Comput. Appl. Math. , 192 : 310 – 319 .
   Google Scholar
• Zhong , H. 2001 . Triangular differential quadrature and its application to elastostatic analysis of Reissner plates . Int. J. Solids Struct. , 38 : 2821 – 2832 .
   Web of Science ®Google Scholar