Two Alternating Direction Implicit Difference Schemes for Solving the Two-Dimensional Time Distributed-Order Wave Equations

2016 ◽  
Vol 69 (2) ◽  
pp. 506-531 ◽  
Author(s):  
Guang-hua Gao ◽  
Zhi-zhong Sun
Keyword(s):  
Wave Equations ◽  
Difference Schemes ◽  
Two Dimensional ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Implicit Difference Schemes ◽  
Distributed Order

scholarly journals New schemes for a two-dimensional inverse problem with temperature overspecification

2001 ◽  
Vol 7 (3) ◽  
pp. 283-297 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Inverse Problem ◽  
Finite Difference ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Central Processor ◽  
Two Dimensional ◽  
Alternating Direction Implicit ◽  
Fully Implicit ◽  
Implicit Schemes ◽  
Alternating Direction

Two different finite difference schemes for solving the two-dimensional parabolic inverse problem with temperature overspecification are considered. These schemes are developed for indentifying the control parameter which produces, at any given time, a desired temperature distribution at a given point in the spatial domain. The numerical methods discussed, are based on the (3,3) alternating direction implicit (ADI) finite difference scheme and the (3,9) alternating direction implicit formula. These schemes are unconditionally stable. The basis of analysis of the finite difference equation considered here is the modified equivalent partial differential equation approach, developed from the 1974 work of Warming and Hyett [17]. This allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes. These schemes use less central processor times than the fully implicit schemes for two-dimensional diffusion with temperature overspecification. The alternating direction implicit schemes developed in this report use more CPU times than the fully explicit finite difference schemes, but their unconditional stability is significant. The results of numerical experiments are presented, and accuracy and the Central Processor (CPU) times needed for each of the methods are discussed. We also give error estimates in the maximum norm for each of these methods.

Three-Point Combined Compact Alternating Direction Implicit Difference Schemes for Two-Dimensional Time-Fractional Advection-Diffusion Equations

2015 ◽  
Vol 17 (2) ◽  
pp. 487-509 ◽  
Author(s):  
Guang-Hua Gao ◽  
Hai-Wei Sun
Keyword(s):  
Diffusion Equations ◽  
Two Dimensional ◽  
Analysis Method ◽  
Order Accuracy ◽  
Alternating Direction Implicit ◽  
Truncation Errors ◽  
Advection Diffusion ◽  
Alternating Direction ◽  
Implicit Difference Schemes ◽  
Adi Schemes

AbstractThis paper is devoted to the discussion of numerical methods for solving two-dimensional time-fractional advection-diffusion equations. Two different three-point combined compact alternating direction implicit (CC-ADI) schemes are proposed and then, the original schemes for solving the two-dimensional problems are divided into two separate one-dimensional cases. Local truncation errors are analyzed and the unconditional stabilities of the obtained schemes are investigated by Fourier analysis method. Numerical experiments show the effectiveness and the spatial higher-order accuracy of the proposed methods.

scholarly journals Pedestrian Walking Behavior Revealed through a Random Walk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Hui Xiong ◽  
Liya Yao ◽  
Huachun Tan ◽  
Wuhong Wang
Keyword(s):  
Numerical Experiments ◽  
Flow Simulation ◽  
Two Dimensional ◽  
Pedestrian Flow ◽  
Alternating Direction Implicit Method ◽  
Walking Behavior ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Continuous Time Random Walks ◽  
High Order Compact Scheme

This paper applies method of continuous-time random walks for pedestrian flow simulation. In the model, pedestrians can walk forward or backward and turn left or right if there is no block. Velocities of pedestrian flow moving forward or diffusing are dominated by coefficients. The waiting time preceding each jump is assumed to follow an exponential distribution. To solve the model, a second-order two-dimensional partial differential equation, a high-order compact scheme with the alternating direction implicit method, is employed. In the numerical experiments, the walking domain of the first one is two-dimensional with two entrances and one exit, and that of the second one is two-dimensional with one entrance and one exit. The flows in both scenarios are one way. Numerical results show that the model can be used for pedestrian flow simulation.

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