Convergence Analysis Of Crank-Nicolson/sinc-collocation Method For A Class Of Partial Integral Differential Equationsn

Fourth-order partial integro-differential equations have important practical significance in many fields such as finance,engineering and biomedicine.With the wide application and rapid development of fractional calculus in many scientific fields,many scholars at home and abroad have proposed different numerical methods to solve fourth-order partial integro-differential equations.For example,finite difference method,finite element method,variational method,orthogonal spline method,homotopy perturbation method,spectral method,domain decomposition method,etc.In this paper,the sinc-collocation method is used to solve fourth-order integro-differential equations with weak singular kernels.Firstly,the Crank-Nicolson method is used to give the time semi-discrete scheme of the equation in the time direction,the sinccollocation method is used in the space direction,and the integral term is discretized by the piecewise constant method.Then the convergence of the full discrete scheme is proved.Finally,several numerical examples are given.The feasibility and efficiency of the sinc-collocation method are verified by comparing the exact solution with the numerical solution.