The Variable Limit Integral Method Of Solving Partial Differential Equations And Its Application

Partial differential equations are ubiquitous in real life.The analytical solutions of most partial differential equations are difficult to obtain.To start with,according to the wave equation,the variable limit integral method for discrete schemes is constructed and the error is calculated.It also gives an explanation on the convergence of the format of the structure.After that,the method of approximate the function of two elements is given in detail.Based on the Taylor expansion of the multivariate function,using the combination of function values at some point,the approximation function of the derivative at the Taylor expansion point is calculater.At the same time,the three element approximation function is introduced briefly.On this basis,this paper uses the variable limit integral method and the approximation function of multivariate function obtained by Taylor expansion in order to analysis hyperbolic diffusion equation.The paper proposes the discrete schemes for hyperbolic diffusion equation,constructed both seven point and nine point scheme.Meanwhile,according to the theory,the stability analysis is given and alos the error is estimated.Numerical cases can reflect the using of the combination of these two methods can provided the discrete schemes for the equations.Moreover the format still can guarantee certain accuracy.Meanwhile,based on the two-dimensional convection diffusion equation,the discrete scheme is constructed by using the Lagrange interpolation method and the Taylor expansion function approximation method.And this paper makes the variable limit integral method more useful.Finally,by using the variational integral method,the wave equation is constructed by using the Taylor expansion function approximation method.According to the one-dimensional convection diffusion equation,the discrete scheme is proposed to facilitate the parallel computation.