Abstract—This paper aims to apply the High Order Explicit Finite Difference Method to solve the famous Nonlinear 1D Burgers Equation in many orders in time (first, second, third and fourth), changing the order on space twice (second and fourth). Thereby, it was compared the results and it was found the best refinement. Thus, it is expected that this work not only can present or even confirm that in most cases greater refinements imply better numerical precision, but rather serve as a basis for decision-making when analyzing the best spatial and should be considered for numerical accuracy and low computational time.

Index Terms—Burgers equation, numerical simulation, numerical efficiency, transient state, explicit finite difference.

Letícia Helena Paulino de Assis, Estaner Claro Romão are with University of São Paulo, Engineering School of Lorena, Environmental and Basic Sciences Department, São Paulo, Brazil (email: estaner23@usp.br, leticia.hpa@alunos.eel.usp.br).

Cite: Letícia Helena Paulino de Assis, Estaner Claro Romão, "Numerical Simulation by High-Order Explicit Finite Difference Method to Solve the Burgers Equation," International Journal of Applied Physics and Mathematics vol. 9, no. 3, pp. 135-143, 2019.