Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions

• Main Authors: Muhammad Amin, Muhammad Abbas, Muhammad Kashif Iqbal, Dumitru Baleanu
• Format: Article
• Language: English
• Published: Frontiers Media S.A. 2020-09-01
• Series: Frontiers in Physics
• Subjects: redefined extended cubic B-spline; time fractional Klein-Gorden equation; Caputo fractional derivative; finite difference method; convergence analysis
• Online Access: https://www.frontiersin.org/article/10.3389/fphy.2020.00288/full

In this article we develop a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution of the time-fractional Klein–Gordon equation. The proposed technique employs the finite difference formulation to discretize the Caputo fractional time derivative of order α ∈ (1, 2] and uses redefined extended cubic B-spline functions to interpolate the solution curve over a spatial grid. A stability analysis of the scheme is conducted, which confirms that the errors do not amplify during execution of the numerical procedure. The derivation of a uniform convergence result reveals that the scheme is O(h2 + Δt2−α) accurate. Some computational experiments are carried out to verify the theoretical results. Numerical simulations comparing the proposed method with existing techniques demonstrate that our scheme yields superior outcomes.