Soliton and Numerical Solutions of the Burgers' Equation and Comparing them

One-dimensional Burgers’ equation is a nonlinear partial differential equation that is a simple form of Navier-stocks equations. Burgers’ equation is known as a model equation, and that is why it is important. This equation has different types and each of them has special applications. Burgers’ equation and their solutions have been discussed in this paper. Analytical solution of this equation includes soliton solution which introduces two basic elements of solution and their application. Their application is used in Burgers’ equation, and the soliton’s solution is obtained from this equation. Numerical methods used in this paper include 8-point and 12-point numerical methods which are multisymplectic. In this paper, by considering different values of soliton’s solution parameters, a comparison is made between 8-point and 12point numerical methods. The error results are calculated through Norm2 and Norm infinity which are shown in the tables. Moreover, the error curves are shown in the tables as well.