NUMERICAL SOLUTION OF FRACTIONAL RELAXATION–OSCILLATION EQUATION USING CUBIC B-SPLINE WAVELET COLLOCATION METHOD

Abstract

A relaxation oscillator is a kind of oscillator based on a behavior of physical system’s return to equilibrium after being disturbed.  The relaxation-oscillation equation is the primary equation of relaxation and oscillation processes.  The relaxation-oscillation equation is a fractional differential equation with initial conditions.  In this paper, the approximate solutions of relaxation-oscillation equation are obtained by developing the wavelet collocation method to fractional differential equations using cubic B-spline wavelet.  Analytical expressions of fractional derivatives in caputo sense for cubic B-spline functions are presented.  The main advantage of the proposed method is that it transforms such problems into a system of algebraic equations which is suitable for computer programming.  The reliability and efficiency of the proposed method are demonstrated in the numerical examples.