CONVERGENCE TEST FOR THE EXTENDED 3 - POINT SUPER CLASS OF BLOCK BACKWARD DIFFERENTIATION FORMULA FOR INTEGRATING STIFF IVP
In this work, a new scheme is generated from the extended 3–point super class of block backward differentiation formula for integrating stiff IVP and the proposed method is subjected to convergence test. The proposed scheme is found to be zero stable, consistent and of order 5. Thus, possess all the required criteria for convergence. The scheme can approximate the values of three points at a time per integration step. The scheme maintained the same technique of co-opting a stability control parameter () in the formula and by adjusting its value within the interval , more A-stabled schemes can be generated. However, this research considers and arrived at zero and A– Stabled method, capable of solving any stiff IVPs. Hence, the proposed convergent scheme can be used for integrating stiff IVPs and archives accuracy of scale error and less executional time.
Curtiss C.F. and Hirschfelder J.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 stoff IVPs in ODE and DAEs." Computational and Applied Mathematics 125, 117-130. DOI: https://doi.org/10.1016/S0377-0427(00)00463-5
Henrici, P. (1962); Discrete Variable Methods in ODEs. New York: John Wiley
Ibrahim, Z. B., Othman, K., and 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
Sulaiman M.B, Musa H, Ismail F. Senu and Ibrahim Z.B. (2013), 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
Musa, H., Suleiman, M. B., Ismail, F.,Senu, N, Majid and Z. A., and brahim, 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, and 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 and 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 and 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 and 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, Shamsuddeen Suleiman, Sagir A.M, and 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 and 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 and Bashir Sule (2022) A New Block of Higher Order Hybrid Super Class BDF for Simulating Stiff IVP Of ODEs. QuestJournals (Journal of Research in Applied Mathematics). 8(12): 50 – 60.
Abdullahi M, G.I. Danbaba and 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
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 and Sirisena U.W (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.
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