Numerical approximations of time fractional multi dimensional Burger's
equation using time-space pseudospectral method
Abstract
In this paper, the authors approximate the solution of time fractional
multi- dimensional Burger’s equation using the time-space Chebyshev
pseudospectral method. Caputo fractional derivatives formula is used to
illustrate the fractional derivatives matrix at CGL points. Using the
Chebyshev fractional derivatives matrices the given problem is reduced
to a system of nonlinear algebraic equations. These equations can be
solved using Newton’s iterative method. Error analysis of the proposed
method for the equation is presented. Model examples of time-fractional
Burger’s equation are tested for a set of values of $
\nu $, where $ \nu $ represent the
fractional order. For the proposed method, highly accurate numerical
results are obtained which are compared with the analytical solution to
confirm the accuracy and efficiency of the proposed method.