Radial Kernels Collocation Method for the Solution of Volterra Integro-Differential Equations

Authors

  • Stephen Mkegh Nengem Taraba State University Jalingo, Nigeria https://orcid.org/0000-0002-1723-7915
  • Friday Haruna Taraba State University Jalingo, Nigeria
  • Shalom Danjuma Bitrus Taraba State University Jalingo, Nigeria

DOI:

https://doi.org/10.54327/set2024/v4.i2.160

Keywords:

Radial Kernel, Volterra Integro-Differential Equations, Generalized Multi-quadrics, Linear Laguerre Gaussians, Collocation Method, System Matrix

Abstract

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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Published

11.10.2024

Data Availability Statement

All sources of data and information used for this research have been duely acknowlewdged and a list of reference provided.

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Section

Research Article

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How to Cite

[1]
S. M. Nengem, F. . Haruna, and S. D. . Bitrus, “Radial Kernels Collocation Method for the Solution of Volterra Integro-Differential Equations”, Sci. Eng. Technol., vol. 4, no. 2, pp. 115–122, Oct. 2024, doi: 10.54327/set2024/v4.i2.160.

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