High Accuracy Numerical System for Fourth-order Fractional Diffusion-wave Model

2018 ◽  
Author(s):  
Xuhao Li ◽  
Patricia J. Y. Wong
Keyword(s):  
Fourth Order ◽  
Wave Model ◽  
Fractional Diffusion ◽  
High Accuracy ◽  
Diffusion Wave ◽  
Diffusion Wave Model

scholarly journals A Mixed Element Algorithm Based on the Modified L1 Crank–Nicolson Scheme for a Nonlinear Fourth-Order Fractional Diffusion-Wave Model

2021 ◽  
Vol 5 (4) ◽  
pp. 274
Author(s):  
Jinfeng Wang ◽  
Baoli Yin ◽  
Yang Liu ◽  
Hong Li ◽  
Zhichao Fang
Keyword(s):  
Fourth Order ◽  
Mixed Finite Element ◽  
Calculated Data ◽  
Coupled System ◽  
Wave Model ◽  
Fractional Diffusion ◽  
Second Order ◽  
Diffusion Wave ◽  
Nicolson Scheme ◽  
Crank Nicolson

In this article, a new mixed finite element (MFE) algorithm is presented and developed to find the numerical solution of a two-dimensional nonlinear fourth-order Riemann–Liouville fractional diffusion-wave equation. By introducing two auxiliary variables and using a particular technique, a new coupled system with three equations is constructed. Compared to the previous space–time high-order model, the derived system is a lower coupled equation with lower time derivatives and second-order space derivatives, which can be approximated by using many time discrete schemes. Here, the second-order Crank–Nicolson scheme with the modified L1-formula is used to approximate the time direction, while the space direction is approximated by the new MFE method. Analyses of the stability and optimal L2 error estimates are performed and the feasibility is validated by the calculated data.

On the diffusion wave model for overland flow: 2. Steady state analysis

1988 ◽  
Vol 24 (5) ◽  
pp. 745-754 ◽  
Author(s):  
R. S. Govindaraju ◽  
S. E. Jones ◽  
M. L. Kavvas
Keyword(s):  
Steady State ◽  
Overland Flow ◽  
Wave Model ◽  
Diffusion Wave ◽  
Steady State Analysis ◽  
Diffusion Wave Model ◽  
State Analysis
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