1Assistant Professor, Department of Applied Science and Humanities, I.T.S. Engineering College, Greater Noida, 201304, Uttar Pradesh, India
2Research-Scholar, Assistant Professor, Department of Applied Mathematics, School of Vocational Studies and Applied Sciences, Gautam Buddha University, Greater Noida, 201310, Uttar Pradesh, India
3Assistant Professor, Department of Applied Mathematics, School of Vocational Studies and Applied Sciences, Gautam Buddha University, Greater Noida, 201310, Uttar Pradesh, India
4Assistant Professor, Department of Mechanical Engineering, School of Engineering, Gautam Buddha University, Greater Noida, 201310, Uttar Pradesh, India
*(*Corresponding Author) E-mail Id: sushil12@gmail.com, sushil.kumar@gbu.ac.in
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.
MQ/IMQ RBFs, Perturbation parameter, Shape parameter, condition number, convective-diffusion equation, elliptic equation, SPP
