Finite Difference Numerical Methods For Parabolic Problems With Nonlocal Boundary Conditions

In this paper,we mainly study two kinds of nonlocal parabolic problems by using the finite difference method.Firstly,the types of non-local problems and the corresponding numerical methods are briefly summarized.Secondly,we give the basic lemmas and proofs of the two kinds of nonlocal parabolic problems.Then,the discrete difference schemes for these two kinds of nonlocal parabolic problems are given,and the local truncation error of the discrete difference scheme is obtained by using the Taylor formula.Then the discrete Fourier transform method is used to estimate the error,and the concrete calculation method of approximate solution is given.Finally,we give the numerical experiments and the results of the analysis of these two kinds of nonlocal parabolic problems,and verify the correctness of the theoretical analysis.