Lax-Wendroff method

 

* The Lax-Wendroff second-order scheme follows from a Taylor series retaining the three terms:

           .         

                   

   

* The first temporal derivative in the above equations is directly replaced using the differential equation. But the second-derivative term is examined in more detail. Considering the original equation and taking its time derivative in the form:

          ,              ,             

                       

          where

* Making the substitution yields

           .         

  

                            

* Using central differencing for derivatives, the Lax-Wendroff second-order numerical scheme is obtained:

   .    

 

 

* Making the substitution yields

           .                     

         

* Using central differencing for derivatives, the Lax-Wendroff second-order numerical scheme is obtained:

          .                  

 

* The Jacobian matrix is computed at the half interval as                                           

* In Burgers’ equation,  and , therefore