Numerical Approach for Solving Stiff Differential Equations: A Comparative Study

Sharaban Thohura; Azad Rahman

Numerical Approach for Solving Stiff Differential Equations: A Comparative Study

Sharaban Thohura * §

Contact

Azad Rahman §

Contact

§ Jagannath University

Numerical Approach for Solving Stiff Differential Equations: A Comparative Study

Article Fingerprint

ReserarchID

94AQ2

Numerical Approach for Solving Stiff Differential Equations: A Comparative Study Banner

Key Research Insights

Synthesized scholarly intelligence & interactive research assistant

This converted HTML version may contain rendering inconsistencies. Please refer to the PDF for the authoritative version, or click here to provide feedback.

Abstract

In this paper our attention is directed towards the discussion of phenomenon of stiffness and towards general purpose procedures for the solution of stiff differential equations. Our aim is to identify the problem area and the characteristics of the stiff differential equations for which the equations are distinguishable. Most realistic stiff systems do not have analytical solutions so that a numerical procedure must be used. Computer implementation of such algorithms is widely available e.g. DIFSUB, GEAR, EPISODE etc. The most popular methods for the solution of stiff initial value problems for ordinary differential equations are the backward differentiation formulae (BDFs). In this study we focus on a particularly efficient algorithm which is named as EPISODE, based on variable coefficient backward differentiation formula. Through this study we find that though the method is very efficient it has certain problem area for a new user. All those problem area have been detected and recommended for further modification.

References

7 Cites in Article

Reference Format

1. L Lapidus,W Schiesser (1976). Numerical Methods For Differential System. Numerical Methods For Differential System
2. L Shampine,C Gear (1979). A user's View of Solving Stiff Ordinary Differential Equations. SIAM Review, 21(1), 1-17.
3. George Byrne,A Hindmarsh (1986). Stiff ODE Solvers: A review of current and coming attractions. Journal of Computational Physics, 70(1), 1-62.
4. R Burden,J Faires (1989). Recommended Resources in Numerical Analysis Kendall Atkinson. Using the Mathematics Literature, 287-314.
5. F Gerald,Wheatley Curtis,Patrick (1999). Applied Numerical Analysis. Applied Numerical Analysis
6. W Enright,T Hull (1976). Comparing Numerical Methods for the Solution of Stiff Systems of ODEs Arising in Chemistry. Numerical Methods for Differential Systems, 45-66.
7. C Gear (1969). NUMERICAL INTEGRATION OF STIFF ORDINARY DIFFERENTIAL EQUATIONS. Report No. 221. Information Processing, 68, 187-193.

Download References

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

Ethical Approval

No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

How to Cite This Article

Sharaban Thohura, Azad Rahman. 2013. "Numerical Approach for Solving Stiff Differential Equations: A Comparative Study". Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 13 (GJSFR Volume 13 Issue 26 (F6)).

More Citation Formats

Select Citation Style:

Download Citation

GJSFR Volume 13 Issue 26 (F6)

Explore Journals Explore Volume Read This Issue

Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

recommended for further modification

Classification

GJSFR-F Classification MSC 2010: 12H20

Submission ReceivedMay 16, 2013
Peer Review Double Blind
Handling Editor
Accepted June 7, 2013
Published June 5, 2013

Version of record

v1.2

Issue date

June 5, 2013

Language

English

Order Article Reprint

Experience in AR

Explore published articles in an immersive Augmented Reality environment. Our platform converts research papers into interactive 3D books, allowing readers to view and interact with content using AR and VR compatible devices.

View in VR

Read in 3D

Your published article is automatically converted into a realistic 3D book. Flip through pages and read research papers in a more engaging and interactive format.

View in 3D

Article Matrices

Total Score: 102

Country: Bangladesh

Subject: Global Journal of Science Frontier Research - F: Mathematics & Decision

Authors: Sharaban Thohura, Azad Rahman (PhD/Dr. count: 0)

View Count (all-time): 299

Total Views (Real + Logic): 1158

Total Downloads (simulated): 93

Publish Date: 2013 05, Fri

Monthly Totals (Real + Logic):

Month 1: 29 views
Month 2: 57 views
Month 3: 28 views
Month 4: 60 views
Month 5: 57 views
Month 6: 43 views
Month 7: 25 views
Month 8: 33 views
Month 9: 45 views
Month 10: 58 views
Month 11: 33 views
Month 12: 36 views
Month 13: 30 views
Month 14: 29 views
Month 15: 30 views
Month 16: 36 views
Month 17: 44 views
Month 18: 29 views
Month 19: 22 views
Month 20: 39 views
Month 21: 14 views
Month 22: 18 views
Month 23: 23 views
Month 24: 13 views
Month 25: 16 views
Month 26: 21 views
Month 27: 39 views
Month 28: 42 views
Month 29: 33 views
Month 30: 36 views
Month 31: 30 views
Month 32: 24 views
Month 33: 19 views
Month 34: 32 views
Month 35: 28 views
Month 36: 44 views
Month 37: 34 views
Month 38: 32 views
Month 39: 32 views
Month 40: 43 views
Month 41: 36 views
Month 42: 32 views
Month 43: 48 views
Month 44: 29 views
Month 45: 32 views
Month 46: 27 views
Month 47: 33 views
Month 48: 46 views
Month 49: 31 views
Month 50: 39 views
Month 51: 37 views
Month 52: 27 views
Month 53: 27 views
Month 54: 25 views
Month 55: 42 views
Month 56: 28 views
Month 57: 25 views
Month 58: 33 views
Month 59: 29 views
Month 60: 35 views
Month 61: 19 views
Month 62: 13 views
Month 63: 36 views
Month 64: 38 views
Month 65: 33 views
Month 66: 35 views
Month 67: 39 views
Month 68: 46 views
Month 69: 12 views
Month 70: 42 views
Month 71: 36 views
Month 72: 35 views
Month 73: 11 views
Month 74: 31 views
Month 75: 37 views
Month 76: 17 views
Month 77: 42 views
Month 78: 13 views
Month 79: 17 views
Month 80: 39 views
Month 81: 33 views
Month 82: 41 views
Month 83: 26 views
Month 84: 30 views
Month 85: 30 views
Month 86: 27 views
Month 87: 40 views
Month 88: 38 views
Month 89: 12 views
Month 90: 44 views
Month 91: 18 views
Month 92: 29 views
Month 93: 15 views
Month 94: 42 views
Month 95: 16 views
Month 96: 44 views
Month 97: 39 views
Month 98: 15 views
Month 99: 19 views
Month 100: 35 views
Month 101: 32 views
Month 102: 34 views
Month 103: 38 views
Month 104: 21 views
Month 105: 32 views
Month 106: 48 views
Month 107: 26 views
Month 108: 19 views
Month 109: 40 views
Month 110: 29 views
Month 111: 23 views
Month 112: 39 views
Month 113: 36 views
Month 114: 18 views
Month 115: 25 views
Month 116: 35 views
Month 117: 36 views
Month 118: 42 views
Month 119: 15 views
Month 120: 44 views
Month 121: 32 views
Month 122: 31 views
Month 123: 28 views
Month 124: 29 views
Month 125: 24 views
Month 126: 27 views
Month 127: 12 views
Month 128: 46 views
Month 129: 38 views
Month 130: 42 views
Month 131: 18 views
Month 132: 25 views
Month 133: 36 views
Month 134: 14 views
Month 135: 37 views
Month 136: 20 views
Month 137: 14 views
Month 138: 40 views
Month 139: 27 views
Month 140: 19 views
Month 141: 37 views
Month 142: 20 views
Month 143: 35 views
Month 144: 30 views
Month 145: 37 views
Month 146: 41 views
Month 147: 26 views
Month 148: 43 views
Month 149: 55 views
Month 150: 24 views
Month 151: 27 views
Month 152: 14 views
Month 153: 57 views
Month 154: 33 views
Month 155: 50 views
Month 156: 43 views
Month 157: 45 views
Month 158: 47 views
Month 159: 31 views
Month 160: 63 views
Month 161: 36 views
Month 162: 15 views

Total Views: 1.2K

Total Downloads: 93

All Trends