# Solving Stiff Ordinary Differential Equations Using Extended Block Backward Differentiation Formulae

• Siti Ainor Mohd Yatim
• Zarina Bibi Ibrahim
• Khairil Iskandar Othman
• Mohamed Suleiman
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 229)

## Abstract

A comprehensive research on the existing Block Backward Differentiation Formulae (BBDF) was done. Based on the suitability in solving stiff ordinary differential equations (ODEs), BBDF of order 3 up 5 is collected using simplified strategy in controlling the step size and order of the method. Thus, Extended Block Backward Differentiation Formulae (EBBDF) is derived with the intention of optimizing the performance in terms of precision and computation time. The accuracy of the method are investigated using linear and non linear stiff initial value problems and its performance is compared with MATLAB’s suite of ODEs solvers namely ode15s and ode23s.

### Keywords

BDF methods Block methods Initial value problem  Numerical analysis Ordinary differential equations Stiff ODEs

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## Authors and Affiliations

• Siti Ainor Mohd Yatim
• 1
• Zarina Bibi Ibrahim
• 2
• Khairil Iskandar Othman
• 3
• Mohamed Suleiman
• 2
1. 1.School of Distance EducationUniversiti Sains Malaysia USMPenangMalaysia
2. 2.Department of MathematicsUniversiti Putra Malaysia UPMSerdangMalaysia
3. 3.Department of MathematicsUniversiti Teknologi MARAShah AlamMalaysia