DEVELOPMENT AND ANALYSIS OF NEW APPROXIMATION OF EXTENDED CUBIC B-SPLINE TO THE NONLINEAR TIME FRACTIONAL KLEIN–GORDON EQUATION

Abstract

A new extended cubic B-spline (ECBS) approximation is formulated, analyzed and applied to obtain the numerical solution of the time fractional Klein–Gordon equation. The temporal fractional derivative is estimated using Caputo’s discretization and the space derivative is discretized by ECBS basis functions. A combination of Caputo’s fractional derivative and the new approximation of ECBS together with [Formula: see text]-weighted scheme is utilized to obtain the solution. The method is shown to be unconditionally stable and convergent. Numerical examples indicate that the obtained results compare well with other numerical results available in the literature.