5ff780a6-4652-4a50-9a49-8ef7f8a1581f20220524085627486wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON FLUID MECHANICS2224-347X1790-508710.37394/232013http://wseas.org/wseas/cms.action?id=40363120223120221710.37394/232013.2022.17https://wseas.com/journals/fluids/2022.phpBlock Solver for Multidimensional Systems of Ordinary Differential EquationsJimevwo GodwinOghonyonDepartment of Mathematics, Covenant University, Km 10. Idiroko, Canaan Land, Ota, Ogun State, NIGERIASolomon AdewaleOkunugaDepartment of Mathematics, University of Lagos Lagos State, NIGERIAPeter OluwatomiOgunniyiDepartment of Mathematics, Covenant University Km 10. Idiroko, Canaan Land Ota, Ogun State, NIGERIAThis research study aimed at developing block solver for multidimensional systems (BSMS) of ordinary differential equations. This method will be formulated via interpolation and collocation techniques with multinomial as the basis function approximate. The block solver has the capacity to utilize each principal local truncation errors to generate the convergence criteria that will ensure convergence. Some theoretical properties will be stated. The process for executing the block solver will be done via the idea of the convergence criteria introduced. Step by step implementation algorithm will be specified. Some selected model applications will be worked out and a suitable step size will be determined to satisfy the convergence criteria in order to enhance the accuracy and efficiency of the method. The implementation of BSMS is coded in Mathematica and executed under the platform of Mathematica Kernel 9.5242022524202289969https://wseas.com/journals/fluids/2022/a185113-006(2022).pdf10.37394/232013.2022.17.9https://wseas.com/journals/fluids/2022/a185113-006(2022).pdfM. L. Abell, J. P. Braselton, Differential equations with Mathematica, Elsevier Academic Press, USA, 2004. 10.1016/j.camwa.2012.03.111O. A. Akinfenwa, S. N. Jator, N. M. 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Lambert, Numerical methods for ordinary differential systems, John Wiley & Sons, New York, 1991. 10.1063/1.4801110A. A. M. N. Nor, B. I. Zarina, I. O. Khairil, S. Mohamed, Numerical solution of first order stiff ordinary differential equations using fifth order block backward differentiation formulas, Sains Malaysiana, Vol. 41, No. 4, 2012, pp. 489-492. J. G. Oghonyon, S. A. Okunuga, N. A. Omoregbe, O. O. Agboola, A computational approach in estimating the amount of pond and determining the long time behavioural representation of pond pollution, Global Journal of Pure and Applied Mathematics, Vol. 11, No 5, 2015, pp. 2773-2785. J. G. Oghonyon, J. Ehigie, S. K. Eke, Investigating the convergence of some selected properties on block predictor-corrector methods and it’s applications, Journal of Engineering and Applied Sciences, Vol. 11, No 11, 2402-2408, 2016. 10.3923/ajsr.2018.553.559J. G. Oghonyon, O. A. Adesanya, H. Akewe, H. I. Okagbue, “Softcode of multi-processing Milne’s device for estimating first-order ordinary differential equations, Asian Journal of Scientific Research, Vol. 11, No. 4, 2018, pp. 553-559. J. G. Oghonyon, O. F. Imaga, P. O. Ogunniyi, The reversed estimation of variable step size implementation for solving nonstiff ordinary differential equations, International Journal of Civil Engineering and Technology, Vol. 9, No. 8, 2018, pp. 332-340. J. G. Oghonyon, S. A. Okunuga, H. I. Okagbue, Expanded trigonometrically matched block variable-step-size technics for computing oscillating vibrations, Proceedings of the International Multi-Conference of Engineerings and Computer Scientists, Vol. 2019, 2019, pp. 552-557. 10.1063/1.4801110B. Zarina, I. Khairil, O. Iskandar, Parallel block backward differentiation formulas for solving large systems of ordinary differential equations, World Academic of Science, Engineering and Technology, Vol. 4, No. 4, 2010, 1-4.