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  and  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, ,  in the list of publications.