Numerical Solution Of Dimension Reduction Model Of KdVB Equation Based On POD Method

In recent years,in the fields of natural science and social science,the influence of nonlinear problems of equations is increasing.For these nonlinear problems,it is necessary to establish nonlinear partial differential equations to solve.The nonlinear partial differential equations studied in this paper are: The Korteweg-de Vries-Burgers(KdVB)equation.In the physical sense,the KdVB equation contains both damping and dispersion,and is a widely used model equation for nonlinear systems.It not only plays an important role in physics,but also It has high research value in applied mathematics.In recent years,many researchers have studied the shape of the solution of the KdVB equation from the mathematical theory and physics,and there are many numerical solutions to the KdVB equation,such as finite element method,tanh method,the hyperbolic tangent method,the exponential rational function method and the finite difference format method.This paper mainly introduces the numerical solution of dimension reduction model of KdVB equation based on POD method.Proper Orthogonal Decomposition(POD)is a method that provides an effective approximation to a large amount of data.Excellent approximation method.The POD method is the most commonly used dimensionality reduction model and is a very efficient method.Its function is to reduce the dimension of the high-dimensional physical process and show the physical characteristics with a relatively low degree of freedom,thereby achieving simplification.Physical model,the purpose of saving computation time and computational load.In this paper,the B-spline Galerkin finite element method and POD dimensionality reduction method for KdVB equations are studied.First,the semi-discrete and full discrete schemes of KdVB are given,and the dimensionality reduction model of KdVB equation is given by using eigenorthogonal decomposition.Secondly,The stability and error estimation of the corresponding method are analyzed.Finally,the effectiveness of the proposed method is verified by numerical calculation.