MAPLE SIMULATION CODES FOR STABILITY ANALYSIS OF VARIABLE STEP SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR INTEGRATING A SYSTEM OF FIRST ORDER STIFF IVPS

  • Muhammad Abdullahi
  • Abdullahi Bello
  • Garba Ismail Danbaba
Keywords: A - Stability, Simulation Code, Maple, Stiff IVPs, Zero Stability

Abstract

Strength of numerical scheme is rated by the properties it possessed and in turn the kind of problems it can handle. Zero stable method can effectively handle ODEs problem. While, an A – stable method can solve stiff ODEs problem. Analyzing stability of block methods are been carried out using various software. This work aimed at using simplified Maple simulation code to critically analyze avariable step size multi-block backward differentiation formula for the solution stiff initial value problems of ordinary differential equations. The Graphical comparisons of the simulated result obtained is made using Matlab to depict the performing schemes.

References

Curtiss C.F. and HirschfelderJ.O. (1952). Integration of Stiff Equations. Proceedings of the National Academy of Sciences, 38, 235-243. DOI: https://doi.org/10.1073/pnas.38.3.235

Cash, J. R. (1980). On the integration of stiff systems of ODEs using extended backward differentiation formulae. NumerischeMathematik. 34: 235-246. DOI: https://doi.org/10.1007/BF01396701

Cash, J. R. (2000). Modified extended backward differentiation formula for the numerical solution of stoffIVPs in ODE and DAEs." Computational and Applied Mathematics 125, 117-130. DOI: https://doi.org/10.1016/S0377-0427(00)00463-5

Ibrahim, Z. B., Othman, K.,& Suleiman, M.B. (2007). Implicit r-point block backward differentiation formula for solving first- order stiff ODEs. Applied Mathematics and Computation, 186, 558-565. DOI: https://doi.org/10.1016/j.amc.2006.07.116

SulaimanM.B, Musa H, Ismail F. Senu, Ibrahim Z.B. (2013a), A new super class of block backward differentiation formula for stiff ODEs, Asian European journal of Mathematics. Vol. 7(1): 1350034–17. DOI: https://doi.org/10.1142/S1793557113500344

Hira Soomro, Nooraini Zainuddin, Hanita Daud, Joshua Sunday, Noraini Jamaludin, Abdullah Abdullah, Apriyanto Mulono, Evizal Abdul Kadir (2022); 3-Point block backward differentiation formula with an of-step point for the solutions of stif chemical reaction problems. Journal of Mathematical Chemistry https://doi.org/10.1007/s10910-022-01402-2 DOI: https://doi.org/10.1007/s10910-022-01402-2

M. B. Suleiman, H. Musa, F. Ismail, and N. Senu (2013b) A new variable step size block backward differentiation formula for solving stiff initial value problems,” International Journal of Computer Mathematics, 11(4): 2391-2408. DOI: https://doi.org/10.1080/00207160.2013.776677 DOI: https://doi.org/10.1080/00207160.2013.776677

Musa, H., Suleiman, M. B., Ismail, F.,Senu, N, Majid and Z. A., Ibrahim, Z. B. (2014). A new fifth order implicit block method for solving first order stiff ordinary differential equations. Malaysian Journal of Mathematicam Sciences 8(S): 45-59.

H. Musa, A.M. Unwala (2019); Extended 3 point super class of block backward differentiation formula for solving first order stiff initial value problems. Abacus (Mathematics Science Series) Vol. 44, No 1, Aug. 2019. DOI: https://doi.org/10.59568/JASIC-2022-3-2-01

A.M. Sagir, Abdullahi, M, (2022) A Robust Diagonally Implicit Block Method for Solving First Order Stiff IVP of ODEs. Applied Mathematics and Computational Intelligence. Volume 11, No.1, [252-273].

A.M. Sagir, Abdullahi, M, (2023a) A Variable Step Size Multi-Block Backward Differentiation Formula for Solving Stiff Initial Value Problem of Ordinary Differential Equations. Eur. J. Stat. 3(4): 1 – 18. DOI: https://doi.org/10.28924/ada/stat.3.4

A.M. Sagir, Abdullahi, M, Ibrahim Muhammad (2023b) A New Hybrid Block Method for Integrating Stiff IVP of ODEs. International Journal of Advances in Engineering and Management (IJAEM) Volume 5(1): 437-447.

Abdullahi M, G.I. Danbaba, Sameer Abdulsaeed (2023) A New Multi-Block Super Class of BDF for Integrating First order Stiff IVP of ODEs. Current Research in Interdisciplinary Studies 2(1): 59-71. DOI: https://doi.org/10.58614/cris214

Abdullahi M, Shamsuddeen Suleiman, SagirA.M, Bashir Sule (2022); An A-stable block integrator scheme for the solution of first order system of IVPs of ordinary differential equations. Asian Journal of probability and statistics. 16(4):11-28. DOI: https://doi.org/10.9734/ajpas/2022/v16i430407

Abdullahi M, Musa, H (2021); Order and Convergence of the enhanced 3 point fully implicit super class of block backward differentiation formula for solving first order stiff initial value problems. Fudma journal of science (FJS). 5(2): 579-584. DOI: https://doi.org/10.33003/fjs-2021-0501-603

Abdullahi M., G.I. Danbaba, Bashir Sule (2022) a New Block of Higher Order Hybrid Super Class BDF for Simulating Stiff IVP Of ODEs. Quest Journals (Journal of Research in Applied Mathematics). 8(12): 50 – 60.

Zawawi, I. S. M., Ibrahim, Z. B., Ismail, F. and Majid, Z. A. (2012). Diagonally implicit block backward differentiation formula for solving ODEs. International journal of mathematics and mathematical sciences. Article ID 767328 DOI: https://doi.org/10.1155/2012/767328

Fatokun J, Onumanyi P, Sirisena UW. (2005) Solution of Ordinary System of Ordinary Differential Equations by Continuous Finite Difference Methods with Arbitrary Basis Functions.J. Nig. Math. Society ; 24:31 –36.

A.A. Nasarudin, Z.B. Ibrahim, H. Rosali, On the integration of stif ODEs using block backward differentiation formulas of order six. Symmetry 12(6), 952 (2020) DOI: https://doi.org/10.3390/sym12060952

Published
2023-08-30
How to Cite
AbdullahiM., Bello A., & Danbaba G. I. (2023). MAPLE SIMULATION CODES FOR STABILITY ANALYSIS OF VARIABLE STEP SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR INTEGRATING A SYSTEM OF FIRST ORDER STIFF IVPS. FUDMA JOURNAL OF SCIENCES, 7(4), 113 - 121. https://doi.org/10.33003/fjs-2023-0704-1905