WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 21, 2022
The Local Nonpolynomial Splines and Solution of Integro-Differential Equations
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Abstract: The application of the local polynomial splines to the solution of integro-differential equations was regarded in the author’s previous papers. In a recent paper, we introduced the application of the local nonpolynomial splines to the solution of integro-differential equations. These splines allow us to approximate functions with a presribed order of approximation. In this paper, we apply the splines to the solution of the integro-differential equations with a smooth kernel. Applying the trigonometric or exponential spline approximations of the fifth order of approximation, we obtain an approximate solution of the integro-differential equation at the set of nodes. The advantages of using such splines include the ability to determine not only the values of the desired function at the grid nodes, but also the first derivative at the grid nodes. The obtained values can be connected by lines using the splines. Thus, after interpolation, we can obtain the value of the solution at any point of the considered interval. Several numerical examples are given.
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Keywords: Local nonpolynomial splines, local trigonometric splines, local exponential splines, integro-differential equation, the fifth order of approximation
Pages: 718-730
DOI: 10.37394/23206.2022.21.84