Solving Singularly Perturbed Problems Using Multi-quadric/Inverse Multi-quadric Radial Basis Function Method

Abstract

This work focuses on the implementation of a multi-quadric/inverse multi-quadric (MQ/IMQ) radial basis function method on Singularly Perturbed Problems (SPP). Elliptic equation and convection–diffusion differential equation are solved using MQ/IMQ RBF methods and results are compared with analytical results. Numerical results are computed using stationary approximation and non-stationary approximation for SPP problems. Condition number of the system matrix in both cases is tuned with shape parameters. Maximum error is reduced for small shape parameter although it is depending on the perturbation parameter. Accuracy and CPU time are computed with increasing the number of distinct centres with a given shape parameter also. Better accuracy is obtained in the case of elliptic SPP as compared to convective–diffusion SPP for a very small perturbation parameter.