A quasi-interpolation method for solving stiff ordinary differential equations

Based on the idea of quasi-interpolation and radial basis functions approxi mation, a numerical method is developed to quasi-interpolate the forcing te rm of differential equations by using radial basis functions. A highly accu rate approximation for the solution can then be obtained by solving the cor responding fundamental equation and a small size system of equations relate d to the initial or boundary conditions. This overcomes the ill-conditionin g problem resulting from using the radial basis functions as a global inter polant. Error estimation is given for a particular second-order stiff diffe rential equation with boundary layer. The result of computations indicates that the method can be applied to solve very stiff problems. With the use o f multiquadric, a special class of radial basis functions, it has been show n that a reasonable choice for the optimal shape parameter is obtained by t aking the same value of the shape parameter as the perturbed parameter cont ained in the stiff equation. Copyright (C) 2000 John Wiley & Sons, Ltd.