|dc.description||Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, Kenya||en_US
|dc.description.abstract||The 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.sponsorship||University of Kwa-Zulu Natal, South Africa.
University of Eswatini, Eswatini.||en_US
|dc.subject||Spectral collocation method||en_US
|dc.subject||Partial differential equations||en_US
|dc.title||Switching between dimensions in spectral collocation method of solution for partial differential equations||en_US