Analysis of New RBF-FD Weights, Calculated Based on Inverse Quadratic Functions

Local radial basis functions (RBFs) have many advantages for solution of differential equations. In some these functions, there is a parameter that has special effect on the accuracy answer and known as shape parameter. this article, first all, we derive inverse quadratic (IQ)-based RBF-generated finite difference coefficients derivatives in one dimension (1D). Then, to evaluate efficiency new weights also resulting approximations, will test them with suitable function. After that, focus solving boundary value problems (BVPs), using IQ-based RBF-FD method. There range which approximation error less than other areas. We use an efficient algorithm find best RBF problem domain. Our studies show could be derived analytically easier multiquadrics (MQs) were previously presented literature. Besides, results numerical examples confirm high formulas. For better comparison, revisit studied illustrative examples.