PAPER TITLE :BLOCK MULTISTEP METHOD FOR THE DIRECT SOLUTION OF THIRD ORDER OF ORDINARY DIFFERENTIAL EQUATIONS

FUTA JOURNAL OF RESEARCH IN SCIENCE | VOLUME 9 NUMBER 2 2013

Paper Details

  • Author(s) : B. T. Olabode
  • Abstract:

This paper presented the direct block multistep method for solving third order initial value problems in ordinary
differential equations. Method of collocation and interpolation of power series approximate solution was used to derive a
continuous linear multistep method. Block method was later used to generate the non-overlapping solution at selected
grid points. The method is self-starting, not requiring developing separate predictors to implement it and it is better than
the conventional predictor-corrector (P-C) methods. Of great interest are some basic properties of the new block
multistep method, such as, convergence, order, error constant and zero-stability. These basic properties were
investigated. The performance of the new block method was tested with some third order initial value problems.
Keywords: Linear multistep methods (LMMs); Zero-stability; Third order; Initial Value Problems (IVPs); Ordinary
Differential Equations (ODEs); Interval of periodicity; Predictor-corrector (P-C)