In this work, we present a solution to a major problem that most researchers meet, which is the solution of differential equations of different dimensions by presenting a new structure to n-dimensions for the Extended cubic B-spline collocation algorithm. The Extended cubic B-spline collocation forms are displayed in one, two and three dimensions. These constructs are of prime importance in solving mathematical models that have applications in various sciences. The efficiency and accuracy of these algorithms through a few test problems in two and three dimensions. Also, comparing our solutions and with the results obtained by using other numerical methods available in the literature as much as possible.