Please use this identifier to cite or link to this item: http://repository.futminna.edu.ng:8080/jspui/handle/123456789/27881
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dc.contributor.authorAudu, Khadeejah James-
dc.date.accessioned2024-05-04T13:26:45Z-
dc.date.available2024-05-04T13:26:45Z-
dc.date.issued2023-06-23-
dc.identifier.citationAudu, K. J. (2023). Numerical Solution of Parabolic Partial Differential Equations via Conjugate Gradient Technique. Paper presented at the 40th Annual Conference of Nigerian Mathematical Society (NMS), Usman Danfodio University, Sokoto, Sokoto State, Nigeria, June 18-23, 2023.en_US
dc.identifier.urihttp://repository.futminna.edu.ng:8080/jspui/handle/123456789/27881-
dc.descriptionA conference paper presentationen_US
dc.description.abstractParabolic partial differential equations (PPDEs) arise in many areas of science and engineering, including heat transfer, diffusion, and fluid dynamics. Analytical solutions to these PPDEs are often difficult or impossible to obtain, so numerical methods are needed to approximate the solution. In this research, we investigate the use of the conjugate gradient technique for numerically solving parabolic PDEs. The technique involves discretizing the PPDE with regard to both space and time. The parabolic partial differential equations are then transformed into systems of linear algebraic equations using the Crank-Nicholson centred difference approach. Then, these equations are solved to yield the unknown points in the grids, which are subsequently substituted into the assumed solution to obtain the required estimated solution, which is reported in tabular format. A comparison was made between the conjugate gradient solutions and those produced using the Jacobi preconditioned conjugate gradient technique in terms of the time required and rate of convergence at that point. Results indicate that conjugate gradient techniques are suitable for solving parabolic-type partial differential equations, with Jacobi-preconditioned conjugate gradient technique converging faster. This research has potential applications in various areas of science and engineering where parabolic PDEs arise.en_US
dc.description.sponsorshipself sponsoren_US
dc.language.isoenen_US
dc.publisherNigeria Mathematical Society (NMS), Nigeriaen_US
dc.subjectParabolic PDEs, convergence, conjugate gradient approach,en_US
dc.subjectpreconditioned conjugate gradient technique, Crank-Nicholson approachen_US
dc.titleNumerical Solution of Parabolic Partial Differential Equations via Conjugate Gradient Techniqueen_US
dc.typePresentationen_US
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