An investigation of resolution of 2-variate Gibbs phenomenon

In this paper, we consider an implementation approach of a method for the resolution of the Gibbs phenomenon for f(x,y) which has been discussed extensively by Jung and Shizgal [J.-H. Jung, B.D. Shizgal, Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon, J. Comput. Appl. Math. 172 (2004) 131-151; J.-H. Jung, B.D. Shizgal, Inverse polynomial reconstruction of two dimensional Fourier images, J. Sci. Comput. 25(3) (2005) 367-399; B.D. Shizgal, J.-H. Jung, Towards the resolution of the Gibbs phenomenoa, J. Comput. Appl. Math. 161 (2003) 41-65]. Here we go through some details of applying that technique and also we try to work out its application on some time-dependent partial differential equations. Numerical experiments confirm the efficiency of the method.