The Simulation By Using Bivariate Splines For Solving Two Dimensional Non-classical Diffusion Problem

Nonlinear partial differential equations have important applications in many fields.The non-classical diffusion problems under two non-local boundary constraints are a kind of nonlinear partial differential equations,which has important research value in physics.The spline method is a classical numerical calculation method,which has been widely used in numerical solutions differential equations and computational geometry.In this paper,a spline method for solving two-dimensional non-classical diffusion problems is proposed.This method first constructs a binary spline subspace S42,3;0(?mn(2))that satisfies the homogeneous boundary condition.We use the Galerkin method to discretize the time-variant boundaries of the two-dimensional non-classical diffusion problem,and then select the functions with finite terms in the sample strip space to superimpose them.It is then required that the weighted integral of the result in the domain and on the boundary conditions satisfy the original equation,so that we can obtain a set of linear equations that are easy to solve and get an approximate solution.Finally,the accuracy of the method is evaluated by solving two examples.The results obtained by the simulation show that the spline method is reliable,and they are consistent with the exact solution other existing numerical methods.