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.