Improved multiquadric approximation for partial differential equations

Based on the idea of the DRM, a numerical method has been devised to interpolate the forcing term of partial differential equations by using multiquadric approximations, a special class of radial basis functions, and then use them to approximate particular solutions. To obtain a good shape parameter of the multiquadrics, we use the technique of cross validation. After we find a particular solution, we then use the method of fundamental solutions to solve the homogeneous PDEs. To demonstrate the effectiveness of our method, four numerical results, including a 3D case, are given. Copyright (C) 1996 Elsevier Science Ltd.