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Numerical simulation of the nonlinear generalized time‐fractional Klein–Gordon equation using cubic trigonometric B‐spline functions
Author(s) -
Yaseen Muhammad,
Abbas Muhammad,
Ahmad Bashir
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6798
Subject(s) - mathematics , discretization , trigonometry , nonlinear system , convergence (economics) , mathematical analysis , numerical analysis , fractional calculus , klein–gordon equation , trigonometric functions , stability (learning theory) , geometry , physics , quantum mechanics , machine learning , computer science , economics , economic growth
In this paper, an efficient numerical procedure for the generalized nonlinear time‐fractional Klein–Gordon equation is presented. We make use of the typical finite difference schemes to approximate the Caputo time‐fractional derivative, while the spatial derivatives are discretized by means of the cubic trigonometric B‐splines. Stability and convergence analysis for the numerical scheme are discussed. We apply our scheme to some typical examples and compare the obtained results with the ones found by other numerical methods. The comparison shows that our scheme is quite accurate and can be applied successfully to a variety of problems of applied nature.