Convergence analysis and parity conservation of a new form of a quadratic explicit spline

TL;DR

This paper introduces a new quadratic spline with explicit coefficients, analyzes its convergence and parity conservation, and applies it to solve integral equations, advancing spline-based numerical methods.

Contribution

It presents a novel explicit quadratic spline, analyzes its convergence and parity properties, and demonstrates its application to integral equations.

Findings

Convergence of the new quadratic spline is established.

Parity conservation property is demonstrated.

Method successfully applied to solve integral equations.

Abstract

In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve integral equations.