[01844] Operational Matrix Based Numerical Scheme for Fractional Differential Equations
Session Time & Room : 4E (Aug.24, 17:40-19:20) @G802
Type : Contributed Talk
Abstract : Fractional calculus is active in many engineering and physics disciplines due to their non-local properties. This non integer order derivative performs well in systems where the next state depends not only on the current state but also upon all of its previous states.
Modeling such systems and determining their precise solutions are current research topics of interest. Since finding exact solutions for fractional differential equations is more challenging, developing numerical techniques is a trending research topic. In this paper, we propose the spectral collocation method based on the operational matrix of orthogonal basis polynomials to find the approximate solution of fractional differential equations. Different orthogonal and non orthogonal basis polynomials are considered for the approximation, and a comparative study is made. The operational matrix of fractional order derivatives of basis polynomials is derived as a product of matrices. This matrix together with the collocation method, is employed to transform the fractional differential equations into a set of algebraic equations, which is easier to tackle. The perturbation method is applied to show the stability of the discussed method. The solution achieved by this method is more precise than those obtained from the existing methods like the variational iterational, adomian decomposition method, and finite difference method.
