An efficient numerical method for the solution of initial and boundary values problems

In this paper, the Multiquadric method (MQ) is used for the numerical solution of ordinary differential equations (ODEs) and partial differential equations (PDEs). In addition, the MQ method is presented for the solution of linear and nonlinear initial value problems. The numerical results show that the MQ method has a higher degree of accuracy with respect to Runge-Kutta method and the other methods. MQ has an exponential accuracy and is more efficient than the finite difference method.