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Vol.26, Special Issue B, 2026, pp. S42–S52 |
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OVERLAPPING MULTI-DOMAIN PAIRED QUASILINEARISATION TECHNIQUE APPLIED TO THE MIXED CONVECTIVE FLOW OF JEFFREY NANOFLUID WITH MICROORGANISM AND ACTIVATION ENERGY Mpho Mendy Nefale1 1) School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, SOUTH AFRICA M.M. Nefale https://orcid.org/0000-0003-2045-9313 ; O. Otegbeye https://orcid.org/0000-0003-1321-9776 *email: olumuyiwa.otegbeye@wits.ac.za 2) School of Technology, Pandit Deendayal Energy University, Gandhinagar 382421, INDIA Md Sharifuddin Ansari https://orcid.org/0000-0002-9277-0904 , **email: md.sharifuddin@spt.pdpu.ac.in 3) Department of Mathematics, Rhodes University, Makhanda, PO Box 94, Grahamstown 6140, SOUTH AFRICA S.D. Oloniiju https://orcid.org/0000-0002-9794-8580
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Abstract This paper presents an innovative numerical technique, the overlapping multi-domain paired quasilinearisation OMD-PQLM, developed for solving highly nonlinear systems of coupled partial differential equations (PDEs). The OMD-PQLM is based on a strategy in which the equations are paired and treated concurrently, thereby improving computational performance through a reduction in the dimension of the coefficient matrix to be inverted while maintaining the high accuracy associated with spectral-based decoupling methods. The approach entails partitioning the entire computational interval of integration into multiple smaller, overlapping subintervals. Solutions in each subinterval are acquired using boundary conditions and solutions from preceding subdomains. To assess the performance of the proposed technique, an analysis is performed on the governing differential equations. The mathematical model describes a Jeffrey nanofluid characterised by active energy and microorganisms within a mixed convection flow environment. The innovation of the OMD-PQLM provides a new understanding of numerical efficiency by merging overlapping multi-domain techniques with the paired quasilinearisation method (PQLM), which improves solution accuracy and convergence. The findings demonstrate that the OMD-PQLM provides highly accurate results, achieving rapid convergence with errors reaching as low as 10–14. Residual and solution error analyses validate the method’s effectiveness and robustness. Flow characteristics concerning controlling parameters are thoroughly analysed, offering valuable insights into the system’s physical behaviour, especially the novelty of the model involving motile microorganisms. The study shows that the OMD-PQLM serves as an effective tool for addressing the nonlinear PDEs that often define complex phenomena within engineering research. Keywords: • Jeffrey nanofluid • bioconvection • activation energy • overlapping subdomains • paired quasilinearisation, spectral method |
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