Qualocation Methods for Time Dependent Partial Differential Equations

The quadrature based collocation method (called as qualocation) was    introduced by Ian Sloan [Numer. Math. 1990] for integral and boundary     integral equations. Subsequently, Sloan et. al. [IMA J. Numer. Anal. 1994] have extended the analysis to two point boundary value problems. To expand its scope, we have generalised the results to parabolic partial differential equations and also have obtained some superconvergence results in [38] and [27] in the list of publications. This also improves upon the results of Sloan et al. in the context of two point boundary value problems. The above analysis is recently extended to the wave equations, partial integro-differential equations     and some nonlinear problems, [27], [33] in the list of publications.