TWO IMPLICIT–EXPLICIT DIFFERENCE SCHEMES FOR A TIME-FRACTIONAL VISCOUS WAVE EQUATION ARISING IN GEOPHYSICS

Jianxiong Cao and Shiyong Li ()
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Jianxiong Cao: Department of Mathematics, School of Sciences, Lanzhou University of Technology, Lanzhou 730050, P. R. China
Shiyong Li: Department of Mathematics, School of Sciences, Lanzhou University of Technology, Lanzhou 730050, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 06, 1-16

Abstract: A time-fractional viscous wave equation Dtαu(x,t) − v2∂ x2u(x,t) − η∂ t∂x2u(x,t) = f(x,t) (1 < α < 2) is considered in this paper, where Dtα is the time Caputo fractional derivative. To solve the equation numerically, we propose two implicit–explicit (IMEX) time-stepping difference schemes. The convergence and unconditional stability of the proposed schemes are strictly proved by using energy method. Numerical experiments illustrate the flexibility and efficiency of the IMEX schemes and also show that they are effective for two-dimensional problems.

Keywords: Time-Fractional Viscous Wave Equation; IMEX Difference Scheme; Stability; Convergence (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401292

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