An Efficient Spline Collocation Method for a Nonlinear Fourth-Order Reaction Subdiffusion Equation

Abstract

The nonlinear fourth-order reaction–subdiffusion equation whose solutions display a typical initial weak singularity is considered. A new analytical technique is introduced to analyze orthogonal spline collocation (OSC) method based on L1 scheme on graded mesh. By introducing a discrete convolution kernel and discrete fractional Gronwall inequality, convergence of the scheme is proved rigorously. This novel analytical technique can provide new insights in analyzing other time fractional fourth-order differential equations with weakly singular solutions.