On A comparison of numerical solutions for Burgers equation

IV SUMMARY Masters Thesis ON A COMPARISON OF NUMERICAL SOLUTIONS FOR BURGERS EQUATION Asıf YOKUŞ Fırat University Graduate School of Natural and Applied Sciences Department of Mathematics 2002, Page : 74 In this work, we apply a relatively new decomposition scheme to solve the linear partial differential equation. The approach is based on the choice of a suitable differential operator which may be ordinary or partial, linear or nonlinear, deterministic or stochastic. It does not require discretization and consequently of massive computation. In this scheme the solution is performed in the form of a convergent power series with easily computable components. The numerical results demonstrate that the new method is relatively accurate and easily implemented. Also in this study, the decomposition method for solving the linear heat equation and nonlinear Burgers equation is implemented with appropriate initial conditions. The application of the method is demonstrated that the partial solution in the x-direction requires more computational work if compared with the partial solution developed in the /-direction but the numerical solution in the x-direction are performed extremely well in terms of accuracy and efficiency. KEY WORDS : Burgers equation, heat equation, Cole-Hopf transformation, Fourier transformation, Adomian's Decomposition method, Adomian polynomials.