On a class of numerical integration methods for a problem of plate deflection theory

References

• Babuska , I. , Prager , M. and Vitasek , E. 1966 . Numerical Processes in Differential Equations , New York : John Wiley (Interscience publishers) .
   Google Scholar
• Fischer , C.F. and Usmani , R.A. 1969 . Properties of some tridiagonal matrices and their applications to boundary value problems . SIAM J. Numer. Anal , 6 : 127 – 142 .
   Web of Science ®Google Scholar
• Fox , L. 1957 . The Numerical Solution of Two-point Boundary Value Problems in Ordinary Differential Equations , London : Oxford University Press .
   Google Scholar
• FröBerg , Carl-Erik. 1969 . Introduction to Numerical Analysis , Reading, Massachusetts : Addison-Wesley .
   Google Scholar
• Henrici , P. 1961 . Discrete Variable Methods in Ordinary Differential Equations , New York : John Wiley .
   Google Scholar
• Jain , M.K. and Iyenger , S.R.K. 1977 . Numerical integration of a fourth order ordinary differential equation . J. Engg. Math , 11 : 373 – 380 .
   Web of Science ®Google Scholar
• Reiss , E.L. , Callegari , A.J. and Ahluwalia , D.S. 1976 . Ordinary Differential Equations with Applications , New York : Holt, Rinehart and Winston .
   Google Scholar
• Timoshenko , S. and Woinowsky-Krieger , S. 1959 . Theory of Plates and Shells , New York : McGraw-Hill .
   Google Scholar
• Usmani , R.A. 1977 . On the numerical solution of a boundary value problem involving a fourth order linear differential equation , B.I.T. 17 : 227 – 234 .
   Google Scholar
• Usmani , R.A. 1978 . On improving error bounds in the integration of a boundary value Problem . Bull. Cal Math. Soc , 70 : 33 – 43 .
   Google Scholar
• Usmani , R.A. . A uniqueness theorem for a boundary value problem . Proceedings of the American Mathematical Society . Vol. 11 , pp. 329 – 335 .
   Google Scholar
• Usmani , R.A. and Marsden , M.J. 1975 . Numerical solution of some ordinary differential equations occurring in plate deflection theory . J. Engg. Math , 9 : 1 – 10 .
   Web of Science ®Google Scholar
• Shoosmith , J.N. August 1973 . “ A study of monotone matrices with an application to the high-order, finite-difference solution of a linear, two-point boundary value problem ” . In Ph.D. dissertation , August , University of Virginia .
   Google Scholar