One of the most challenging PDE forms in fluid dynamics namely Burgers equations is solved numerically in this work. Its transient, nonlinear, and coupling structure are carefully treated. The Hermite type of collocation mesh-free method is applied to the spatial terms and the 4th-order Runge Kutta is adopted to discretize the governing equations in time. The method is applied in conjunction with the Gaussian radial basis function. The effect of viscous force at high Reynolds number up to 1,300 is investigated using the method. For the purpose of validation, a conventional global collocation scheme (also known as “Kansa” method) is applied parallelly. Solutions obtained are validated against the exact solution and also with some other numerical works available in literature when possible.
This study investigates three choices of shape parameter selection when the so-called Radial Basis Function (RBF) is used. Under the problem of pattern recognition via RBF-Neural Network using RC-algorithm, three RBFs are focussed on; Gaussian (GA), Multiquadric (MQ), and Compactly-Supported (CS1). Two pattern recognition cases are tested and the best choice of shape parameter is validated using Model-Selection Criteria (MSC).
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