Numerical solution of fractional relaxation- oscillation equation by using residual power series method

The relaxation oscillator is a type of oscillator that is based on the nature of physical phenomena that tend to return to equilibrium after being distributed. The relaxation-oscillation equation is the primary equation of the process of relaxation-oscillation. In this work, the relaxation-oscillation equation is solved using the residual power series method, which is a fractional order differential equation with defined initial conditions. The results obtained by this method are more reliable and accurate as compared to those obtained by other methods studied previously to solve this equation. The reliability and efficiency of this method are demonstrated by means of three examples with exact solutions compared with approximate solutions by means of errors. The pseudocode of the applied methodology has also been discussed in brief. The residual power series method can be used to solve well-known fractional order differential equations.(c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Automated summary

The relaxation oscillator is an oscillator that returns to equilibrium after being disturbed. This study solves the relaxation-oscillation equation using the residual power series method, which proves to be more reliable and accurate than other methods. The reliability and efficiency of this method are demonstrated through examples and error comparisons. The pseudocode of the method is also discussed briefly. This method can be used to solve fractional order differential equations.