A Crank-Nicolson Approximation for the time Fractional Burgers Equation

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 L2 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.

Integrated neuro-swarm heuristic with interior-point for nonlinear SITR model for dynamics of novel COVID-19

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On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis

“…Fractional differentiation and integration have opened many new doors for researchers in recent decades due to their wide and novel applicability in many fields of science including mathematical analysis, technology, and engineering (see [1][2][3][4][5][6][7]). Many techniques are used to deal with these new differential and integral operators; for instance, some researchers used analytical techniques including Laplace transform, spline interpolation, Green function, Crank-Nicolson approximation method, method of separation of variable, and many others to derive exact solutions to linear differential or integral equations (see [8][9][10][11][12][13][14]). Using the fixed-point technique, some researchers provided the conditions under which differential and integral equations have unique solutions.…”