TY - JOUR
T1 - Numerical Approach of Cattaneo Equation with Time Caputo-Fabrizio Fractional Derivative
TT -
JF - IJMSI
JO - IJMSI
VL - 19
IS - 2
UR - http://ijmsi.ir/article-1-1783-en.html
Y1 - 2024
SP - 127
EP - 153
KW - Caputo-Fabrizio fractional derivative
KW - Compact finite difference
KW - Cattaneo equation
KW - Alternating direction implicit method.
N2 - In the paper, we consider a type of Cattaneo equation with time fractional derivative without singular kernel based on fourth-order compact finite difference (CFD) in the space directions. In case of two dimensional, two alternating direction implicit (ADI) methods are proposed to split the equation into two separate one dimensional equations. The time fractional derivation is described in the Caputo-Fabrizio’s sense with scheme of order O(τ2). The solvability, unconditional stability and H1 norm convergence of the scheme are proved. Numerical results confirm the theoretical results and the effectiveness of the proposed scheme.
M3
ER -