Numerical solution of time fractional non-linear neutral delay differential equations of fourth-order

Sarita Nandal; Dwijendra N Pandey

doi:10.26637/MJM0703/0035

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 $O\left(\tau^2+h^4\right)$, 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, L2-1σ formula, Compact difference scheme, Stability, Convergence

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Sarita Nandal Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India.
Dwijendra N Pandey Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India. https://orcid.org/0000-0001-8542-7094

Pages: 579-589
Date Published: 01-07-2019
Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)

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