Radial Kernels Collocation Method for the Solution of Volterra Integro-Differential Equations
DOI:
https://doi.org/10.54327/set2024/v4.i2.160Keywords:
Radial Kernel, Volterra Integro-Differential Equations, Generalized Multi-quadrics, Linear Laguerre Gaussians, Collocation Method, System MatrixAbstract
Radial kernel interpolation is an advanced method in approximation theory for the construction of higher order accurate interpolants for scattered data up to higher dimensional spaces. In this manuscript, we formulate a radial kernel collocation approach for solving problems involving the Volterra integro-differential equations using two radial kernels: The Generalized Multi-quadrics and the linear Laguerre-Gaussians. This was achieved by simplifying the Volterra integral problem's solution to an algebraic system of equations. The impact of the shape parameter present in every kernel on the method's accuracy is examined and found to be significant. Two examples were used to illustrate the process; the numerical results are shown as tables and graphs. MATLAB 2018a was employed in the process.
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All sources of data and information used for this research have been duely acknowlewdged and a list of reference provided.
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Copyright (c) 2024 Stephen Mkegh Nengem, Friday Haruna, Shalom Danjuma Bitrus
This work is licensed under a Creative Commons Attribution 4.0 International License.
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