Derivation of septic B-spline function in n-dimensional to solve n-dimensional partial differential equations

In this study, a new structure for the septic B-spline collocation algorithm in -dimensional is presented as a continuation of generating B-spline functions in -dimensional to solve mathematical models in -dimensional. The septic B-spline collocation algorithm is displayed in three forms: one dimensional, two dimensional, and three dimensional. In various domains, these constructs are essential for solving mathematical models. The effectiveness and correctness of the suggested method are demonstrated using a few two- and three-dimensional test problems. The proposed new structure provides better results than other methods because it deals with a larger number of points than the field. To create comparisons, we use different numerical approaches accessible in the literature.