Research Projects

Finite difference methods are used to approximate the derivatives of a function at a node, which are expressed as the linear combination of functional values at neighboring nodes multiplied by weights. Implementing these methods on complex domains and unstructured grids is complex, and computing finite difference weights for scattered nodes is a challenge. RBF finite difference methods, developed by Chu and Fan in 1997, can handle this problem by using linear combinations of symmetric radial basis functions. RBF interpolants offer precise approximation of derivatives and manage programming complexity in higher-dimensional problems. The project focuses on developing and analyzing Radial basis function-based CCD schemes, which combine the accuracy of CCD schemes with the flexibility of RBF schemes. This approach helps control programming complexity in higher-dimensional problems.