  The extended definition of the polynomial B-splines may give a chance to
improve the results obtained by the classical cubic polynomial B-splines.
Determination of the optimum value of the extension parameter can be achieved
by scanning some intervals containing zero. This study aims to solve some
initial boundary value problems con- structed for the Gardner equation by the
extended cubic B-spline collocation method.The test problems are derived from
some analytical studies to validate the efficiency and accuracy of the
suggested method. The conservation laws are also determined to observe them
remain constant as expected in theoretical aspect. The stability of the
proposed method is investigated by the Von Neumann analysis.
