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.
Highlights
Fractional order derivatives are considered more appropriate for the interpretation of certain real-life phenomena
The temporal fractional derivative is estimated using Caputo’s discretization and the space derivative is discretized by extended cubic B-spline (ECBS) basis functions
The integer-order derivatives including nonlinear models derived from standard mathematical model do not work in many cases. It has been observed in the recent years, that fractional calculus has become important in various fields such as biology, chemistry, economics, electricity, mechanics, signal and image processing and control theory
Summary
Fractional order derivatives are considered more appropriate for the interpretation of certain real-life phenomena. The integer-order derivatives including nonlinear models derived from standard mathematical model do not work in many cases It has been observed in the recent years, that fractional calculus has become important in various fields such as biology, chemistry, economics, electricity, mechanics, signal and image processing and control theory. A numerical method based on new extended cubic B-spline (NECBS) approximation for the solution of TFKGE is developed. This approximation is used for the second-order derivative in space direction. In order to formulate the new approximation, we will use the linear combination (LC) of ECBS at neighboring points This technique has never been used, as far as we are aware, for the case of nonlinear TFKGE.
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