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

Abstract

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.

Keywords

• Fractional relaxation–oscillation equation
• Residual power series method
• Fractional differential equations
• Exact solutions and approximate solutions