Differential equations are relationships between functions and their derivatives and naturally appear in many disciplines. It is well known that it is not easy to obtain the exact solutions. Therefore, several methods and techniques are available to solve the differential equations.

One method used to find approximate particular solutions is introduced by Kansa; this involves using the radial basis function (RBF), and later it is modified to solve parabolic, hyperbolic, and elliptic partial differential equations (PDEs). In this work, a new neural network method is introduced to approximate the functions and their derivatives. The design of the network is based on the data provided by the PDE and its boundary conditions. Further, the authors provide an algorithm that is based on adaptively inserting knots with different RBFs. This algorithm allows one to obtain a fast and accurate reconstruction of some solutions of particular PDEs.