Cubic B-spline method for non-linear sine-Gordon equation

In this article, one dimensional non-linear sine-Gordon equation has been studied. We propose a new method based on collocation of cubic B spline to find the numerical solution of non-linear sine-Gordon equation with Dirichlet boundary conditions. The method involves high order perturbations of the classical cubic spline collocation method at the partition nodes. The existence and uniqueness of the numerical solution has been proved. The method produces optimal fourth order accurate solutions. Stability analysis of the method has been done. The numerical experiments confirm the expected accuracy. We compare the results obtained by our method with those by other techniques for some already existing examples in the literature.