Derivation of a new block method similar to the block trapezoidal rule for the numerical solution of first-order IVPs

Abstract

In this paper, a new block method of the second order is presented to solve initial value problems numerically. This method is similar to the block trapezoidal rule [S. Abbas and L.M. Delves, Parallel solution of ODE's by one step block methods, Report CSMR, University of Liverpool, 1989.], where the low power of the block size appears in the principal local truncation error. Direct comparison with the related results of the block trapezoidal rule has been outlined.

Keywords:

• block method
• ordinary differential equations
• parallel methods
• predictor-corrector method

2000 AMS Subject Classification :

• 65L05
• 65Y05

Acknowledgements

I am grateful to the referees for very constructive comments and for suggesting various improvements to the manuscript.