Switching between dimensions in spectral collocation method of solution for partial differential equations

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dc.contributor.authorMutua, Samuel
dc.contributor.authorMotsa, Sandile
dc.date.accessioned2021-05-10T14:40:01Z
dc.date.available2021-05-10T14:40:01Z
dc.date.issued2019-08
dc.descriptionPaper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, Kenyaen_US
dc.description.abstractThe key feature in the numerical solution of the differential equations involves the generation of a linear algebraic system of equations from the discretization process. The system of equations is, in turn, solved directly using any mathematics application that supports matrix computations. The complexity of assembling coefficient matrices of the linear algebraic system of equations especially when solving partial differential equations (PDES) is proportional to the number of independent variables involved. Considering a purely spectral collocation type of discretization, numerical solutions for two-dimensional PDEs exists but those of three-dimensional problems are missing. In this work, we aim at demonstrating the construction of a numerical scheme for solving three-dimensional problems using a purely Chebyshev spectral collocation method. First, we review the description of numerical schemes that is well-known for two-dimensional (21)) case, then explore a transition to the three-dimensional (3D) problems. We test the practical applicability of the numerical schemes by solving 21) and 3D problems reported in the literature. Pertinent properties of accuracy, computational efficiency, stability, and convergence of the numerical schemes are analyzed and discussed in graphical and tabular forms.en_US
dc.description.sponsorshipUniversity of Kwa-Zulu Natal, South Africa. University of Eswatini, Eswatini.en_US
dc.identifier.urihttp://hdl.handle.net/11071/11800
dc.publisherStrathmore Universityen_US
dc.subjectSpectral collocation methoden_US
dc.subjectPartial differential equationsen_US
dc.titleSwitching between dimensions in spectral collocation method of solution for partial differential equationsen_US
dc.typeArticleen_US
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