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The lack of reliable judgment on the choice of shape parameter is acknowledged as a drawback in the methodology of collocation meshfree by radial basis function (RBF). Some attempts have been proposed and tested only with specific classes of PDEs. Moreover, while most of this focusses on multiquadric (MQ) RBF, there has not been work done on invers-multiquadric (IMQ) RBF despite its’ increasing popularity. As a consequence, our main tasks in this work are, firstly, to numerically investigate the quality of each adaptive/variable RBF-shape parameter approaches presented in literature by applying them to the same type of problem, convection-diffusion class. Secondly, we proposed a new form of shape-parameter scheme to be used with the inverse-multiquadric (IMQ) type of RBF. The Kansa meshless method is implemented and it is interestingly found that the proposed form produces good results quality in terms of both matrix condition number, and the accuracy.

Solution to a Convection-Diffusion Problem Using a New Variable Inverse-Multiquadric Parameter in a Collocation Meshfree Scheme