Generalization of the Group Classification with Application of Elliptic Partial Differential Equations

This research work enhance the generalizing previous result on a one-dimensional nonlinear elliptic partial differential equation. By the use of new techniques of a partial differential equation with the equivalence of group ,class of group and groupoid, we extend the algebraic method of classification of nonlinear partial differential equations. The solution includes the preliminary group, sub algebras, and infinite-dimensional equivalence algebra. This result is examined by the example of Elliptic partial differential equation.