The use of nonlinear trapezoidal formulae with extrapolation for accurate solutions of initial value O.D.E.s

References

• Evans , D. J. and Sanugi , B. B. 1988 . A nonlinear trapezoidal formula for the solution of initial value problems . Comp. and Maths. Applics. , 15 : 77 – 79 .
   Web of Science ®Google Scholar
• Sanugi B. B. New numerical strategies for initial value type ordinary differential equations Ph.D. Thesis Loughborough University of Technology 1986
   Google Scholar
• Lambert , J. D. 1973 . Computational Methods in Ordinary Differential Equations , London : John Wiley and Sons .
   Google Scholar
• Gragg , W. B. 1965 . On extrapolation algorithms for ordinary initial value problems . SINUM , 2 : 384 – 403 .
   Google Scholar
• Schryer , N. L. 1974 . “ An extrapolation step-size monitor for solving ordinary differential equations ” . In Proc. ACM 140 – 148 .
   Google Scholar
• Bulirsch , R. and Stoer , J. 1966 . Numerical treatment of ordinary differential equations by extrapolation methods . Num. Math. , 8 : 1 – 13 .
   Web of Science ®Google Scholar
• Lambert , J. D. 1973 . Computational Methods in Ordinary Differential Equations , Wiley .
   Google Scholar
• Davis , P. J. 1963 . Interpolation and Approximation Blaisdell
   Google Scholar
• Bulirsh , R. and Stoer , J. 1964 . Fehlerab Schatzungen und Extrapolation mit Rationalen Funletionen bei Verfahren vom Richardson-Typus . Num. Math. , 6 : 413 – 427 .
   Google Scholar
• Steadman J. K. Rational approximation of the solution to a stiff ordinary differential equation using extrapolation Ph.D. Thesis Stevens Institute of Technology 1981
   Google Scholar
• Stoer , J. 1961 . Uber zwei Algorithmen zur Interpolation mit rationalen funktionen . Num. Math. , 3 : 285 – 304 .
   Google Scholar
• Richardson , L. F. 1927 . The deferred approach to the limit . Philos. Trans. Roy. Soc. London , A226 : 299 – 361 .
   Google Scholar