A collocation method using new combined radial basis functions of thin plate and multiquadraic types

The meshless methods for solving boundary value problems have been extensively popularised owing to their flexibility in engineering applications. In the present paper, a meshless method based on a new combination between thin plate and multiquadraic radial basis functions is developed. The new form of the radial basis function contains a parameter ε, which named a control parameter, 0⩽ε⩽10⩽ε⩽1. Starting the proposed method by the classical Θ–weight implicit finite difference approximation, then fellow up the same procedure as thin plate or multiquadraic but with the new form of the radial basis function. The parameter, ε will take zero when evaluating the diagonal elements for the coefficients matrix resulted. Two different examples were solved with different dimensionality and the present results were compared with the analytical results and gave a good agreement.