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

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.

Approximate solutions of one-dimensional systems with fractional derivative

“…Segmentary interpolation is a standard tool of wide use in the approximation of solutions of differential equations [12]. Let us sketch the method here for completeness, using an approach that has been used in previous articles by our group [13,14]. Let [a, b] be a compact interval in the real axis R. At regular intervals, we select n nodes,…”

“…The objective is to obtain an approximation for the solution of equation ( 14) under the condition x(t * ) = x * . We already know how to obtain the identity (14) in the nodes t k . Take these nodes with the exception of t * .…”

“…Let us study the precision of the method with another example different from the fractional oscillator, yet an equation of the form (14). Here, we have chosen,…”