Strict Fourier Convergence Analysis For Linear Equations

To the best of our knowledge,Fourier method is often used for theoretical analysis of discrete schemes.However,we find that the method is too demanding for convergence analysis,which is generally difficult to realize.In this paper,about convergence analysis,based on the idea of Fourier analysis,we give a strict proof that all linear equations with constant coefficients or variable coefficients independent of spatial variables are applicable.Taking the specific fractional equation with variable coefficients as an example,we discuss its difference scheme,and the rigorous theoretical proof is given.Finally,the convergence order measured by the numerical examples is consistent with the theoretical analysis.