Computational Study of Multi-Term Time-Fractional Differential Equations Using Cubic B-spline Finite Element Method

Abstract

Fractional differential equations precisely measure and describe biological and physical processes because of the symmetry feature in nature. Multi-term time-fractional (MTTF) introduced for modeling of complex processes in different physical phenomena. This article introduces a numerical method based on Cubic B-spline (CBS) Finite element method (FEM) for solution of MTTF partial differential equations(PDEs). Finite difference method is combined with theta-weighted scheme and simple quadrature rules are used for time-fractional discretization while CBS FEM is employed for space approximation. In addition, four-point Gauss Legendre quadrature is applied to evaluate the source term. Stability of the proposed scheme is discussed by Von Neumann method which verifies that the scheme is unconditionally stable. L 2 and L ∞ norms are used to check efficiency and accuracy of the proposed scheme. Computed results are compared with the exact and available methods in literature which show betterment of the proposed method.

Computational Study of Multiterm Time‐Fractional Differential Equation Using Cubic B‐Spline Finite Element Method

“…Furthermore, the proposed model is used to discretize distributed-order derivatives in DEs. Hence, studies of multiterm fractional order DEs have become essential and valuable for diferent applications [15,16]. Tis work considers multiterm time-fractional DEs as follows: P α 1 ,α 2 ,...,α m z t 􏼁Y(w, t) � z 2 Y(w, t) zw 2 + f(w, t), (w, t) ∈ (c, d) ×(0, T),…”