A novel quintic B-spline technique for numerical solutions of the fourth-order singular singularly-perturbed problems

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dc.contributor.authorYousaf, Muhammad Zain
dc.contributor.authorSrivastava, Hari Mohan
dc.contributor.authorAbbas, Muhammad
dc.contributor.authorNazir, Tahir
dc.contributor.authorMohammed, Pshtiwan Othman
dc.contributor.authorVivas-Cortez, Miguel
dc.contributor.authorChorfi, Nejmeddine
dc.date.accessioned2024-01-04T19:25:54Z
dc.date.available2024-01-04T19:25:54Z
dc.date.copyright2023en_US
dc.date.issued2023
dc.description.abstractSingular singularly-perturbed problems (SSPPs) are a powerful mathematical tool for modelling a variety of real phenomena, such as nuclear reactions, heat explosions, mechanics, and hydrodynamics. In this paper, the numerical solutions to fourth-order singular singularly-perturbed boundary and initial value problems are presented using a novel quintic B-spline (QBS) approximation approach. This method uses a quasi-linearization approach to solve SSPNL initial/boundary value problems. And the non-linear problems are transformed into a sequence of linear problems by applying the quasi-linearization approach. The QBS functions produce more accurate results when compared to other existing approaches because of their local support, symmetry, and partition of unity features. This method can be applied to immediately solve the SSPPs without reducing the order in which they are presented. It has been demonstrated that the suggested numerical approach converges uniformly over the whole domain. The proposed approach is implemented on a few problems to validate the scheme. The computational results are compared, and they illustrate that the proposed approach performs better.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.identifier.citationYousaf, M. Z., Srivastava, H. M., Abbas, M., Nazir, T., Mohammed, P. O., Vivas-Cortez, M., & Chorfi, N. (2023). A novel quintic B-spline technique for numerical solutions of the fourth-order singular singularly-perturbed problems. Symmetry, 15(10), 1929. https://doi.org/10.3390/sym15101929en_US
dc.identifier.urihttps://doi.org/10.3390/sym15101929
dc.identifier.urihttp://hdl.handle.net/1828/15787
dc.language.isoenen_US
dc.publisherSymmetryen_US
dc.rightsAttribution 2.5 Canada*
dc.rights.urihttp://creativecommons.org/licenses/by/2.5/ca/*
dc.subjectsingular singularly-perturbed non-linear initial/boundary value problems
dc.subjectuniform convergence
dc.subjectfourth-order Emden–fowler type equation
dc.subjectQBS function
dc.subjectfourth-order BVP and IVP
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleA novel quintic B-spline technique for numerical solutions of the fourth-order singular singularly-perturbed problemsen_US
dc.typeArticleen_US

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