A Crank-Nicolson Approximation for the time Fractional Burgers Equation
Mehmet Önal, Alaattin Esen
Abstract
Abstract In the present manuscript, Crank Nicolson finite difference method is going to be applied to get the approximate solutions for the fractional Burgers equation. The fractional derivative used in this equation is going to be taken into consideration in the Caputo sense. The L1 type discretization formula is going to be applied to this equation. For checking the efficiency of proposed methods, the error norms L 2 and L ∞ have at the same time been calculated. Those newly got solutions using the presented method illustrate the easy usage and efficiency of the approach presented in this manuscript.
Topics & Concepts
Burgers' equationFractional calculusCrank–Nicolson methodMathematicsDiscretizationApplied mathematicsType (biology)Mathematical analysisDifferential equationBiologyEcologyFractional Differential Equations SolutionsNumerical methods in engineeringDifferential Equations and Numerical Methods