Development of non polynomial spline and New B-spline with application to solution of Klein-Gordon equation

In this paper we develop a non polynomial cubic spline functions which we called ”TS spline”, based on trigonometric functions. The convergence analysis of this spline is investigated in details. The definition of Bspline basis function for TS spline is extended and ”TS B-spline” is introduced. This paper attempts to develop collocation method based on this B-spline for the numerical solution of the nonlinear Klein-Gordon equation. The convergence analysis of this approach is discussed, the second order of convergence is proved consequently. The proposed method is applied on some test examples and the numerical results are compared with those already available in literature. Observed errors in the solutions show the efficiency and numerical applicability of the proposed method.