A graded scheme with bounded grading for a time-fractional Boussinesq type equation

In this note, we extend our recent work, which studied high-order nonuniform method for a time-fractional nonlinear PDE, to construct a graded linearized scheme for a time-fractional Boussinesq type equation which involved a Caputo derivative of order beta is an element of (1, 2) in time, when the solution is not smooth. We show that the numerical solution converges to the exact solution with temporal third-order accuracy for fitted grading parameter bounded in (1, 1.5). This result is different from previous ones where gradings will tend to infinity. (C) 2019 Elsevier Ltd. All rights reserved.