Applying the Fractional Cubic Spline Method to Solve Dynamic Systems Numerically
DOI:
https://doi.org/10.56714/bjrs.52.1.1Keywords:
Spline approximation, Caputo fractional derivative,, computational modelling, convergence analysis.Abstract
In this work, we present a new numerical technique for solving systems of differential equations in arising dynamical systems that is based on fractional cubic spline interpolation. The spline consists of several dimensions, and one of the fractional dimensions is . In order to estimate the solution of nonlinear or linear dynamical systems, the suggested method builds a fractional cubic spline with suitable continuity and differentiability constraints and applies it iteratively. We can find the results for each step, and the error rate decreases, which in our sample makes the relative error close to However, this method requires tracking the dynamic system at each step, using the previous step, which takes a lot of time. Therefore, we rely on MATLAB here. Better modeling of systems having memory effects or hereditary properties which are prevalent in many physical, biological, and engineering problems is made possible by the addition of fractional variables. The method's correctness and efficacy are demonstrated by numerical trials, which also show strong agreement with analytical or benchmark solutions
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