Asymptotic Stability of Compact and Linear $$\theta $$-Methods for Space Fractional Delay Generalized Diffusion Equation

Investigations for a Type of Variable Coefficient Fractional Subdiffusion Equation with Multidelay

“…We complete the proof. To discuss the stability of the difference schemes (22)- (24), we consider the following problem:…”

“…Now, we present the following numerical tests to testify the schemes ( 22)- (24). Introducing the following notations,…”

“…[15][16][17]. Numerical solutions for FDDEs can be found in [18][19][20][21][22][23][24][25], where [18][19][20] considered numerical solutions for FDDEs, and [21][22][23][24][25] considered numerical solutions for fractional delay partial differential equations (FDPDEs). However, the researchers seldom considered the numerical methods for FDDEs with multidelays; some studies considered such FDDEs without theoretical analysis.…”

A Newton Linearized Crank-Nicolson Method for the Nonlinear Space Fractional Sobolev Equation

“…Zhang et al [11] established the numerical asymptotic stability result of the compact θ -method for the generalized delay diffusion equation. More researches on delay fractional problems can be referred to [12,13] and the references therein.…”

A robust numerical method for a coupled system of singularly perturbed parabolic delay problems

“…In the past two decades, many researchers have paid attention to the field of delay differential equations and have developed various numerical methods, see, e.g. Zhang et al (2016Zhang et al ( , 2017, Zhang and Li (2019), Pimenov et al (2017), Hendy et al (2020), Hendy (2017a, 2017b) and the references therein. Robust numerical methods for scalar singularly perturbed delay ordinary differential equations (ODEs) and PDEs have also been developed extensively in the literature, see, e.g.…”