Corrigendum to “Derivation of Diagonally Implicit Block Backward Differentiation Formulas for Solving Stiff Initial Value Problems”

Iskandar Shah Mohd Zawawi,Khairil Iskandar Othman,Zarina Bibi Ibrahim

doi:10.1155/2017/8791862

Abstract

Corrigendum to “Derivation of Diagonally Implicit Block Backward Differentiation Formulas for Solving Stiff Initial Value Problems”

Highlights

In the fifth paragraph of the “Introduction” section, the sentence “The formulas of fully implicit 2-point block extended backward differentiation formula of order three (FI2BEBDF(3)) and fully implicit 3-point block extended backward differentiation formula of order three (FI3BEBDF(3)) are given in the following forms” should be corrected to “The formulas of fully implicit 2-point block extended backward differentiation formula of order four (FI2BEBDF(4)) and fully implicit 3-point block extended backward differentiation formula of order six (FI3BEBDF(6)) are given in the following forms.” equation (5) shows the “FI2BEBDF(4)” not “FI2BEBDF(3).” equation (6) should be written as follows: FI3BEBDF(6)
In subsection “Computational Time,” the sentence “In Tables [1,2], it can be seen that the execution time taken by DI2BBDF(2), DI2BBDF(3), and DI2BBDF(4) is comparable with that of FI2BBDF(3) and FI2BEBDF(3)” should be changed to “In Tables [1,2], it can be seen that the execution time taken by DI2BBDF(2), DI2BBDF(3), and DI2BBDF(4) is comparable with that of FI2BBDF(3) and FI2BEBDF(4).”
The sentence “Tables [3,4,5,6] show that the proposed methods compute faster than FI3BBDF(3) and FI3BEBDF(3)” should be changed to “Tables [3,4,5,6] show that the proposed methods compute faster than FI3BBDF(3) and FI3BEBDF(6)”

Summary

Methods

MAXE 5.25481E − 3 3.88475E − 3 8.56253E − 5 1.21629E − 4 1.65094E − 4 5.51558E − 5 4.27506E − 5 8.89803E − 9 1.30124E − 8 1.69456E − 8 5.51803E − 7 4.27924E − 7 1.26115E − 11 6.27106E − 11 1.04222E − 11. In subsection “Computational Time,” the sentence “In Tables [1,2], it can be seen that the execution time taken by DI2BBDF(2), DI2BBDF(3), and DI2BBDF(4) is comparable with that of FI2BBDF(3) and FI2BEBDF(3)” should be changed to “In Tables [1,2], it can be seen that the execution time taken by DI2BBDF(2), DI2BBDF(3), and DI2BBDF(4) is comparable with that of FI2BBDF(3) and FI2BEBDF(4).”. The sentence “Tables [3,4,5,6] show that the proposed methods compute faster than FI3BBDF(3) and FI3BEBDF(3)” should be changed to “Tables [3,4,5,6] show that the proposed methods compute faster than FI3BBDF(3) and FI3BEBDF(6)”.