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.

In this work, the study of the Peyrard-Bishop DNA dynamic model equation analytically and numerically will present. The Kudryashov method and modified Kudryashov method are used to nd the solution of the Peyrard-Bishop DNA dynamic model equation analytically. A cubic B-spline collocation method is used to obtain a numerical solution of the Peyrard-Bishop DNA dynamic model equation. A comparison between the results obtained by the analytical methods and the numerical method is investigated. We give some figures to show how accurate the solutions will be obtained from analytical and numerical methods.