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Information Technology Journal

Year: 2012 | Volume: 11 | Issue: 9 | Page No.: 1141-1153
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Authors

R. Ponalagusamy

K. Ponnammal

Keywords

Research Article

Local Truncation Error for the Parallel Runge-Kutta-Fifth Order Methods

R. Ponalagusamy and K. Ponnammal
We derive for the first time, the new mathematical expression for Local Truncation Error (LTE) by using the order trees for the parallel fifth order Runge-Kutta formulae while solving the initial value problem y’ = f (x y), y (x0) = y0. Based on the concept of tree theory, a modest effort has been made to obtain the error coefficients and derivatives of the LTE using the order trees and elementary differentials of the explicit parallel Runge-Kutta fifth order methods. It is shown that the new parallel scheme (PPRKF) compares well with the analytic solution and is often more accurate than other parallel methods (PRKF 1 and PRKF 2). With the help of numerical examples, the absolute error and estimated LTE have been computed.
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