A robust error analysis of the OSC method for a multi-term fourth-order sub-diffusion equation

Abstract

In this paper, we consider an orthogonal spline collocation (OSC) method to solve the fourth-order multi-term subdiffusion equation. The L1 method on graded meshes is employed in temporal direction. In the spatial direction, we develop the orthogonal spline collocation method. The stability and convergence of the above mentioned method are proved theoretically, and it's still valid if α1→1−. A new robust error bound is obtained, which is a more natural and desirable result and does not blow up as α1→1−. Some numerical results are also provided to verify our theoretical analysis and demonstrate the effectiveness of the OSC method.