A Class Of Invariant Difference Schemes For Burgers Equations

To preserve the physical properties of the original equation is the research focus of modern numerical analysis, Lie group method and invariant difference scheme are two important fields. Constructing the discrete schemes according to PDEs’properties and testing the numerical results are very meaningful.First, construct Burgers equation’s invariant difference scheme according to the the (1+1) dimensional Burgers equation’s symmetry; and construct a semi-discrete schemes based on discreted space. Three test problems have been studied to demonstrate the accuracy of the present two methods. The results, which have copared with the exact solution and other numerical method’s results, are found to be in better agreement with exact solution.Second, invariant difference schemes and semi-discrete schemes are obtained according to (2+1) dimensional coupled Burgers equation’s properties. Initial boundary value problems are used to test the accuracy of the two methods.