A NEW SECOND DERIVATIVE METHODS WITH HYBRID PREDICTORS FOR SOLVING STIFF AND NON-STIFF ORDINARY DIFFERENTIAL EQUATIONS

Authors

  • Gilbert A. Akhanolu AMBROSE ALLI UNIVERSITY, EDO STATE
  • Larry O. Adoghe Department of Mathematics, Ambrose Alli University, Ekpoma
  • Luke O. Ukpebor Ambrose Alli University, Ekpoma, Edo State

DOI:

https://doi.org/10.33003/fjs-2024-0804-2405

Keywords:

Power series collocation, interpolation, Hybrid multistep method, Nested

Abstract

This study derives new second derivative linear multistep methods with efficient criteria sufficient for the solvability of the stiff initial value problems by means of interpolation and collocation techniques. The hybrid predictors in the procedure are nested.   The stiff initial value issues in ordinary differential equations were approximated by using power series as the basis function. The method's stability properties were examined and subsequently provided. The region of absolute stability of the novel schemes was studied using the boundary locus method. Through its combination as a block matrix, the resulting approaches are applied to solve a number of stiff initial value issues. The new techniques produced numerical findings and errors that compared favorably with  some existing methods in the literature.

Author Biographies

Gilbert A. Akhanolu, AMBROSE ALLI UNIVERSITY, EDO STATE

Lecturer II in the department of mathematics, AMBROSE ALLI UNIVERSITY, EKPOMA,EDO STATE

Larry O. Adoghe, Department of Mathematics, Ambrose Alli University, Ekpoma

Senior lecturer in the Department of Mathematics, Ambrose Alli University, Ekpoma, 

Luke O. Ukpebor, Ambrose Alli University, Ekpoma, Edo State

Professor in the department of mathematics in the Ambrose Alli University, Ekpoma

References

Akeredolu, F.A. and Sonibare, J. A. (2015). Process evaluation of Nigerian’s artisanal (“illegal”) petroleum refineries for effective air pollution control. In: Proceeding of the 45th Annual conference of NSChE, 5th-7th Nov. Warri, Nigeria, 94-109.

Asuru, C. andAmadi, S. (2016). Technological capability as a critical factor in Nigerian development: the case of indigenous refineries in the Niger Delta region. International Journal of Innovative Research Education, Technology and Social Strategies. 3(1), 2467–8163.

Bebeteidoh, O., Pazuki, K., Kometa, S. and Norman, R. (2020). Sustained impact of the activities of local crude oil refiners on their host communities in Nigeria. Heliyon. 5(6), e04000.

Bond, T. C., Doherty, S. J., Fahey, D. W., Forster, P. M., Berntsen, T., Deangelo, B. J., Flanner, M.G., Ghan, S., Kondo, Y., Quinn, P. K., Sarofim, M. C., Schultz, M. G., Schulz, M., Venkataraman, C., Zhang, H., Zhang, S., Bellouin, N., Guttikunda, S. K., Hopke, P. K., Jacobson, M. Z., Kaiser, J. W., Klimont, Z., Lohmann, U., Schwarz, J. P., Shindell, D., Storelvmo, T. and Warren, S. G. (2013). Bounding the role of black carbon in the climate system: A scientific assessment. Journal of Geophysical Research Atmospheres. 118(11):5380

Emodi, A. 1. And Isife, B. I. (2019). Household perceived effects of black soot on health and agricultural produce in Port Harcourt Metropolis, Rivers State. International Journal of Agricultural and Rural Development. 20(1): 427-435.

Jack J.T.C.B and Zibima, T. (2020). Soot pollution in Rivers State: An analysis of environmental public health impacts and coping strategies. Social Science Review 1(1). 193 -200.

Mamudu A., Okoro, E., Igwilo, K., Olabode, O., Francis, E. and Odunlami, O. (2019). Challenges and prospects of converting Nigeria illegal refineries to modular refineries. The Open Chemical Engineering Journal. 13: 1-6. DOI: 10.2174/1874123101913010001

Miller, K. A., Siscovick, D. S., Sheppard, L., Shepherd, K., Sullivan, J. H. anderson, G. L. and Kaufman, J. D. (2007). Long-term exposure to air pollution and incidence of cardiovascular events in women. New England Journal of Medicine. 356:447-458.

Niessner, R. (2014). The many faces of soot: Characterization of soot Nanoparticles Produced by Engines. Angewandte Chemie International Edition. 53(46):12366-12379

Niranjan, R. and Thakur, A. K. (2017). The toxicological mechanisms of Environmental Soot (Black carbon) and carbon black: Focus on oxidative stress and inflammatory pathways. Frontiers in Immunology. 8:763.

Obi-Udu, I., Uwadiegwu, B.O., Okoye, O.N.N. and Onwuka, S. U. (2022). Study on Heavy Metal Contamination from the Soot of Flared Gas on Selected Vegetation of Jeddo Community, Delta State, Nigeria. British Journal of Environmental Sciences. 10 (6): 66-72.

Omidvarborna H., Kumar, A. and Dong-Shik, K (2015). Recent studies on soot modeling for diesel combustion. Renewable and Sustainable Energy Reviews. 48:635-647.

Onwuna, D.B., Stanley, H.O., Abu, G.O. and Immanuel, O.M. (2022a). Air quality at artisanal crude oil refinery sites in Igia-Ama, Tombia Kingdom, Rivers State, Nigeria. Asian Journal of Advanced Research and Reports. 16(12): 74-83.

Onwuna, D.B., Stanley, H.O., Abu, G.O. and Immanuel, O.M. (2022b). Impact of artisanal crude oil refinery on physicochemical and microbiological properties of soil and water in Igia-Ama, Tombia Kingdom, Rivers State, Nigeria. Asian Journal of Environment and Ecology. 19(3): 56-67. DOI: 10.9734/ajee/2022/v19i3412

Swami, A. (2018): Impact of Automobile Induced Air Pollution on road side vegetation: A Review. Essence Int. J. Env. Rehab. Conserv. 9 (1): 101-116.

Published

2024-08-24

How to Cite

Akhanolu, G. A., Adoghe, L. O., & Ukpebor, L. O. (2024). A NEW SECOND DERIVATIVE METHODS WITH HYBRID PREDICTORS FOR SOLVING STIFF AND NON-STIFF ORDINARY DIFFERENTIAL EQUATIONS. FUDMA JOURNAL OF SCIENCES, 8(4), 193 - 198. https://doi.org/10.33003/fjs-2024-0804-2405