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In this paper, we present a fourth-order finite difference method for solving nonlinear one-dimensional Burgers equation. This method is unconditionally stable, fourth-order accurate in space and second-order accurate in time. Accuracy of the scheme is demonstrated by solving a test problem, and the numerical results obtained by this method for different values of Reynolds number have been compared...
Our focus mainly concerns solving the Hamilton-Jacobin-Bellman (HJB) equations derived from the nonlinear receding horizon control (RHC) schemes. A new numerical methods using the finite difference with sigmoidal transformation for computing the value function is developed. The developed numerical method is a stable and convergent algorithm for HJB equations. A fine optimization procedure is developed...
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