numerical solution of the one dimensional non-linear burgers equation using the adomian decomposition method and the comparison between the modified local crank-nicolson method and the vim exact ‎solution

the burgers’ equation is a simplified form of the navier-stokes equations that very well represents their non-linear features. in this paper, numerical methods of the adomian decomposition and the modified crank – nicholson, used for solving the one-dimensional burgers’ equation, have been compared. these numerical methods have also been compared with the analytical method. in contrast to the conventional crank-nicolson method, the mlcn method is an explicit and unconditionally stable method. the adomian decomposition method includes the unknown function u (x), in which each equation is defined and solved by an infinite series of unbounded functions. velocity parameters u in the direction of the x axis, are examined at different times with different reynolds numbers over a fixed time step. also the accuracy of the adomian and the crank-nicolson methods at different reynolds numbers have been studied using two examples with different initial conditions, and the adomian decomposition method is closer to the analytical ‎method.‎