Fourth-order methods for space fractional reaction–diffusion equations with non-smooth data

We propose two fourth-order methods in time for one-dimensional space fractional reaction–diffusion equations. The methods are based on fourth-order Exponential Time Differencing Runge–Kutta method. Padé approximations of matrix exponential functions are used to construct an L-stable and an A-stable method. Partial fraction splitting technique is applied to construct more reliable and computationally efficient versions of the methods. Solution profiles as well as convergence rates in time are presented for fractional enzyme kinetics equation and fractional Fisher equation. The L-stable method performs well in the presence of non-smooth mismatched initial-boundary data while the A-stable method is more economical for smooth matched initial-boundary data.