Numerical analysis of block-by-block method for a class of fractional relaxation-oscillation equations

Fractional relaxation-oscillation equation (FROE) is an important physical model describing oscillators. Its numerical solution method has profound theoretical significance and application value. In this paper, we use a non-singularity kernel Volterra integral equation of block-by-block method and construct a block-by-block numerical scheme based on Lagrange basis function interpolation. The analysis proves the stability and convergence of the block-by-block method. Error analysis shows that the convergence order is at least 4 which significantly improves calculation accuracy. Through the error comparison, the error of block-by-block method in this paper is significantly lower than that prediction-correction(P-C) method, which overcomes the shortcomings of the existing methods of low accuracy in solving FROE. Both theoretical analysis and numerical experiments show the high accuracy and effectiveness of the block-by-block numerical scheme, which shows that the method in this paper is efficient and feasible to solve the FROE.