A Fourth-order Difference Scheme For A Class Of Fourth-order Partial Integral Differential Equations

The four order problem is widely used in modern science and engineering,after many scholars' research,the four-order differential theory is becoming more and more mature.However,numerical methods and theoretical analysis of four order partial differential equation is a difficult thing,so we should develop effective numerical methods for solving four order partial integral differential equation.We consider a class of four order four order partial differential equation difference scheme,the time direction by two order backward difference,spatial direction by four order difference.The integral item on the first two interpolation time on the integrand approximate integral,get a three level difference scheme for the first time.The numerical solutions of the Crank-Nicolson layer discretization,discretization leads to a relatively simple calculation.Finally,a series of conclusions are obtained by numerical examples,and the convergence order is 2 order by numerical examples.