Total views : 233

### Formulation of Modified Variable Step Block Backward Differentiation Formulae for Solving Stiff Ordinary Differential Equations

#### Affiliations

• School of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
• Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia

#### Abstract

Objectives: A modified variable step block backward differentiation formulae (MVS-BBDF) method is introduced in this paper as another alternative way for solving ordinary differential equations (ODEs). Methods: We demonstrated the detailed formulation of the corrector formulae for MVS-BBDF method which is carried out using Maple software. Then, to validate the performance of the introduced method, we applied it to stiff ODEs problem. Findings: The performance of the method in terms of maximum error and number of total steps taken during the computation are compared with the performance of ode15s and ode23s solver in MATLAB. Consequently, the efficiency of MVS-BBDF shows that it is able to outperform both Matlab’s ODE solver since it produces better accuracy and manages to reduce the number of total step.

#### Keywords

Backward Differentiation Formulae, Block Backward Differentiation Formulae, Stiff Ordinary Differential Equations.

#### Full Text:

|  (PDF views: 192)

#### References

• Finizio N, Ladas G. Ordinary differential equations with modern applications. Wadsworth, Inc.; 1981.
• Birkhoff G, Rota G.C. Ordinary Differential Equations, 5th edn. John Wiley & Sons, Inc.; 1989.
• Myint-U T ed. Ordinary differential equations. Elsevier North-Holland, Inc.; 1987.
• Mahayadin M, Othman KI, Ibrahim ZB. Variable step three-point block methods for solving stiff ordinary differential equations. Computational Methods in Science and Engineering. 80–83.
• Ibrahim ZB, Suleiman M, Othman KI. Fixed coefficients block backward differentiation formulas for the numerical solution of stiff ordinary differential equations. European Journal of Scientific Research. 2008; 21(3):508–20.
• Zawawi ISM, Ibrahim ZB, Othman KI. Derivation of diagonally implicit block backward differentiation formulas for solving stiff initial value problems. Mathematical Problems in Engineering. 2015, 2015.p.1–13.
• Othman KI, Ibrahim ZB, Suleiman M. Parallel block backward differentiation formulas for solving ordinary differential equations. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering. 2008; 2(4):257–59.
• Nasir NAAM, Ibrahim ZB, Suleiman MB. Fifth order twopoint block backward differentiation formulas for solving ordinary differential equations. Applied Mathematical Sciences. 2011;5(71):3505–518.
• Abasi N, Suleiman M, Abbasi N, Musa H. 2-point block BDF method with off-step points for solving stiff ODEs. Journal of Soft Computing and Applications. 2014; 2014.p.1-15.
• Akinfenwa OA, Jator SN, Yao NM. Continuous block backward differentiation formula for solving stiff ordinary differential equations. Computers & Mathematics with Applications. 2013;65:996–1005. Crossref
• Yatim SAM, Ibrahim ZB, Othman KI, Ismail F. Fifth order variable step block backward differentiation formula for solving stiff ODEs. World Academy of Science, Engineering and Technology. 2010;4(2):236–38.
• Ibrahim ZB, Othman KI, Suleiman M. Variable step block backward differentiation formula for solving first order stiff ODEs. Proceedings of the World Congress on Engineering 2007, London: 2007.
• Gear CW. Numerical initial value problems in ordinary differential equations. Prentice Hall, Inc.: New Jersey, 1971. PMCid:PMC1411756
• Gerald CF, Wheatley PO. Applied numerical analysis, Addison Wesley Publishing Company; Boston. 1989. PMCid:PMC2625985

### Refbacks

• There are currently no refbacks.