Curve Fitting Initial Guess for Iterative Differential Quadrature Solution of Burgers Equation

Abstract

According to presented numerical studies in the literature, the solution of Burgers Equation (BE) performed for dt=0.001 and dt=0.0001 commonly. In this study, numerical solution of BE carried out by using the Iterative Differential Quadrature Method (I-DQM), as dt=0.01. Convergence speed and accuracy of iterative methods depends on the initial guess. Every Partial Differential Equation (PDE) describes one or more than one physical problems from the perspective of the engineering view. Unlike the previous iterative studies, in this work, an initial guess value is used in accordance with the physical nature of the discussed problem by using curve fitting. Absolute error analysis of obtained results performed for comparison with some previous studies. The consequence of comparisons shows that more accurate results and faster solution than other studies could be obtained by using I-DQM with curve fitting initial guess.