A generalized form of the parametric spline methods of degree (2k + 1) for solving a variety of two-point boundary value problems

Document Type : Research Article

Author

• Z. Sarvari

Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.

10.22067/ijnao.2023.79288.1192

Abstract

In this paper, a high order accuracy method is developed for finding the approximate solution of two-point boundary value problems. The present approach is based on a special algorithm, taken from Pascal’s triangle, for obtaining a generalized form of the parametric splines of degree (2k + 1), k = 1, 2, . . . , which has a lower computational cost and gives the better ap-proximation. Some appropriate band matrices are used to obtain a matrix form for this algorithm.
The approximate solution converges to the exact solution of order O(h4k ), where k is a quantity related to the degree of parametric splines and the number of matrix bands that are applied in this paper. Some examples are given to illustrate the applicability of the method, and we compare the computed results with other existing known methods. It is
observed that our approach produced better results.

Keywords

• Boundary value problems
• Parametric spline
• Band matrices
• Pascal’s triangle

Main Subjects

• Numerical Analysis

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