Orthogonal spline collocation method for the fourth-order diffusion system

The fourth-order diffusion systems depict the wave and photon propagation in intense laser beams and play an important role in the phase separation in binary mixture. In this paper, by using orthogonal spline collocation (OSC) method in spatial direction and classical L1 approximation in temporal direction, a fully discrete scheme is established for a class of fourth-order fractional reaction-diffusion equations. For the original unknown u and auxiliary variable v=Δu, the full-discrete unconditional stabilities based on a priori analysis are derived by virtue of properties of OSC. Moreover, the convergence rates in L2-norm for unknown u are strictly investigated. At the same time, the optimal error estimates in H1-norm for unknown u and in L2-norm for variable v, are also derived, respectively. For further verifying the theoretical analysis, some numerical examples are provided.