A Stable Finite Volume Method for Numerical Solution of Time-Tempered Fractional Sine–Gordon Equations
摘要
This paper proposes a numerical method based on the finite volume method for solving the time-tempered fractional sine–Gordon equation. To overcome the nonlinearity of the sine–Gordon equation, a fixed-point method is employed to linearize the sine–Gordon equation. Additionally, a novel approach utilizing the Discrete Gronwall Lemma has been introduced to prove the stability of the method. The provided examples demonstrate the effectiveness of the method and validate the presented theory.