Nonstandard finite difference method for solving complex-order fractional Burgers’ equations
N. H. Sweilam, Seham M. Al‐Mekhlafi, Dumitru Bǎleanu
Abstract
The aim of this work is to present numerical treatments to a complex order fractional nonlinear one-dimensional problem of Burgers’ equations. A new parameter σt is presented in order to be consistent with the physical model problem. This parameter characterizes the existence of fractional structures in the equations. A relation between the parameter σt and the time derivative complex order is derived. An unconditionally stable numerical scheme using a kind of weighted average nonstandard finite-difference discretization is presented. Stability analysis of this method is studied. Numerical simulations are given to confirm the reliability of the proposed method.
Topics & Concepts
DiscretizationMathematicsFractional calculusNonlinear systemBurgers' equationStability (learning theory)Applied mathematicsFinite difference methodFinite differenceOrder (exchange)Derivative (finance)Numerical analysisWork (physics)Mathematical analysisPartial differential equationComputer sciencePhysicsThermodynamicsEconomicsQuantum mechanicsFinanceMachine learningFinancial economicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNumerical methods for differential equations