Abstract
In continuation to what we started from developing the B-spline functions and putting them in n-dimensional to solve mathematical models in n-dimensions, we present in this article a new structure for the quintic B-spline collocation algorithm in n-dimensional. The quintic B-spline collocation algorithm is shown in three different formats: one, two, and three dimensional. These constructs are critical for solving mathematical models in different fields. The proposed method's efficiency and accuracy are illustrated by their application to a few two- and three-dimensional test problems. We use other numerical methods available in the literature to make comparisons.