Numerical solution of time fractional non-linear neutral delay differential equations of fourth-order
Authors :
Sarita Nandal 1 * and Dwijendra N Pandey 2
Author Address :
1,2 Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India.
*Corresponding author.
Abstract :
In this paper, we present a numerical technique for the solution of a class of time fractional nonlinear neutral delay sub-diffusion differential equation of fourth order with variable coefficients. We constructed a numerical scheme which is of second-order convergence in time and is based on L2-1$\sigma$ formula for the temporal variable. The stability of the scheme is proved using discrete energy method considering several auxiliary assumptions and then we showed that our scheme is convergent in $L_2$ norm with convergence order $O(\tau^2+h^4)$, where $\tau$ and $h$ are temporal and space mesh sizes respectively. In the end, we provide some numerical experiments to validate the theoretical results.
Keywords :
Fractional differential equation, L2-1$\sigma$ formula, Compact difference scheme, Stability, Convergence.
DOI :
Article Info :
Received : February 12, 2019; Accepted : August 19, 2019.
