A fully discrete difference scheme for a diffusion-wave system

By Zhi‐zhong Sun, Xiaonan Wu. 2006

1,187 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Modeling and Simulation

1. G. Em Karniadakis
2. Bangti Jin
3. Mohsen Zayernouri
4. Mark Ainsworth
5. Lu Lu
6. Yubin Yan
7. Chuanju Xu
8. 许传炬

In Numerical Analysis

1. G. Em Karniadakis
2. Bangti Jin
3. Mohsen Zayernouri
4. Yubin Yan
5. Chuanju Xu
6. 许传炬
7. Mark Ainsworth
8. William Rundell

Citations in the corpus

• fPINNs: Fractional Physics-Informed Neural Networks (2018, methodology): “The truncating error for the L1 scheme is (\Delta t) 2 - \gamma [44].”
• Existence and Uniqueness of the Weak Solution of the Space-Time Fractional Diffusion Equation and a Spectral Method Approximation (2010, background): “[27], Sun and Wu [51], Langlands and Henry [20] and so on.”
• A fast linearized finite difference method for the nonlinear multi-term time-fractional wave equation (2019, methodology): “on the interval [τ, T ], where β ∈ (0, 1) and τ is the time step size, and combined with the classical L1 discretization [13, 22, 32], Jiang et al.”
• A finite element method for time fractional partial differential equations (2011, methodology): “Sun and Wu [31] proposed a finite difference method for the fractional diffusion-wave equation.”
• Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem (2013, methodology): “The existing numerical methods includes finite difference [7,11,19], Galerkin finite element [4, 5, 15], finite difference/spectral method [9], time-space spectral method [8], and so on.”
• Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation (2013, methodology): “Inspired by their work on the weighted and shifted Grünwald difference operator, in this paper, we establish high order schemes for the fractional diffusion-wave equation and the modified anomalous fractional sub-diffusion equation, which were proposed and studied in [8, 9] and [25]–[27], respective”
• Analysis of the compact difference scheme for the semilinear fractional partial differential equation with time delay (2017, neutral): “1: [29] Suppose y(t) ∈ C2[0, tk], Let ∣∣∣∣∣ 1 (1 − γ ) ∫ tk”
• A unified Petrov-Galerkin spectral method for fractional PDEs (2015, background): “We demonstrate that this framework can reduce to hyperbolic FPDEs such as timeand space-fractional advection (TSFA), parabolic FPDEs such as time- and space-fractional diffusion (TSFD) model, and elliptic FPDEs such as fractional Helmholtz/Poisson equations with the same ease and cost.”