Optimal Control Problems Driven by Time-Fractional Diffusion Equations on Metric Graphs: Optimality System and Finite Difference Approximation

SIAM Journal on Control and Optimization ◽

10.1137/20m1340332 ◽

2021 ◽

Vol 59 (6) ◽

pp. 4216-4242

Author(s):

Vaibhav Mehandiratta ◽

Mani Mehra ◽

Gunter Leugering

Keyword(s):

Optimal Control ◽

Finite Difference ◽

Optimal Control Problems ◽

Fractional Diffusion ◽

Finite Difference Approximation ◽

Diffusion Equations ◽

Difference Approximation ◽

Control Problems ◽

Metric Graphs ◽

Fractional Diffusion Equations

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Notes on Implicit finite difference approximation for time fractional diffusion equations [Comput. Math. Appl. 56 (2008) 1138–1145]

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2011.02.051 ◽

2011 ◽

Vol 61 (9) ◽

pp. 2924-2928 ◽

Author(s):

Heng-fei Ding ◽

Yu-xin Zhang

Keyword(s):

Finite Difference ◽

Fractional Diffusion ◽

Finite Difference Approximation ◽

Diffusion Equations ◽

Difference Approximation ◽

Fractional Diffusion Equations ◽

Implicit Finite Difference

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Implicit finite difference approximation for time fractional diffusion equations

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2008.02.015 ◽

2008 ◽

Vol 56 (4) ◽

pp. 1138-1145 ◽

Author(s):

Diego A. Murio

Keyword(s):

Finite Difference ◽

Fractional Diffusion ◽

Finite Difference Approximation ◽

Diffusion Equations ◽

Difference Approximation ◽

Fractional Diffusion Equations ◽

Implicit Finite Difference

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Finite difference schemes for the two-dimensional multi-term time-fractional diffusion equations with variable coefficients

Computational and Applied Mathematics ◽

10.1007/s40314-021-01551-1 ◽

2021 ◽

Vol 40 (5) ◽

Author(s):

Mingrong Cui

Keyword(s):

Finite Difference ◽

Fractional Diffusion ◽

Variable Coefficients ◽

Difference Schemes ◽

Diffusion Equations ◽

Finite Difference Schemes ◽

Two Dimensional ◽

Fractional Diffusion Equations

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A High Order Finite Difference Method for Tempered Fractional Diffusion Equations with Applications to the CGMY Model

SIAM Journal on Scientific Computing ◽

10.1137/18m1172739 ◽

2018 ◽

Vol 40 (5) ◽

pp. A3322-A3343 ◽

Author(s):

Xu Guo ◽

Yutian Li ◽

Hong Wang

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

High Order Finite Difference

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A finite difference scheme for semilinear space-fractional diffusion equations with time delay

Applied Mathematics and Computation ◽

10.1016/j.amc.2015.11.071 ◽

2016 ◽

Vol 275 ◽

pp. 238-254 ◽

Author(s):

Zhaopeng Hao ◽

Kai Fan ◽

Wanrong Cao ◽

Zhizhong Sun

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Semilinear Space

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Finite difference approximations to constrained optimal control problems

Lecture Notes in Control and Information Sciences - Optimization and Optimal Control ◽

10.1007/bfb0004519 ◽

2005 ◽

pp. 243-254 ◽

Author(s):

Kazimierz Malanowski

Keyword(s):

Optimal Control ◽

Finite Difference ◽

Optimal Control Problems ◽

Control Problems ◽

Constrained Optimal Control ◽

Finite Difference Approximations ◽

Difference Approximations

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Numerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularity

Numerical Algorithms ◽

10.1007/s11075-020-00923-8 ◽

2020 ◽

Author(s):

Zhaopeng Hao ◽

Wanrong Cao ◽

Shengyue Li

Keyword(s):

Finite Difference ◽

Dimensional Space ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Two Dimensional ◽

Boundary Singularity ◽

Fractional Diffusion Equations ◽

Finite Difference Solution ◽

Difference Solution

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The Error Analysis of Finite Difference Approximation for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations with Discontinuous Source Term

Finite Difference Methods. Theory and Applications - Lecture Notes in Computer Science ◽

10.1007/978-3-030-11539-5_18 ◽

2019 ◽

pp. 175-184

Author(s):

S. Chandra Sekhara Rao ◽

Sheetal Chawla

Keyword(s):

Finite Difference ◽

Error Analysis ◽

Source Term ◽

Reaction Diffusion ◽

Reaction Diffusion Equations ◽

Singularly Perturbed ◽

Finite Difference Approximation ◽

Diffusion Equations ◽

Difference Approximation ◽

Discontinuous Source Term

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An error estimate for the finite difference approximation to degenerate convection–diffusion equations

Numerische Mathematik ◽

10.1007/s00211-011-0433-9 ◽

2011 ◽

Vol 121 (2) ◽

pp. 367-395 ◽

Author(s):

K. H. Karlsen ◽

U. Koley ◽

N. H. Risebro

Keyword(s):

Finite Difference ◽

Error Estimate ◽

Finite Difference Approximation ◽

Diffusion Equations ◽

Difference Approximation ◽

Convection Diffusion

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A priori error analysis of the upwind symmetric interior penalty Galerkin (SIPG) method for the optimal control problems governed by unsteady convection diffusion equations

Computational Optimization and Applications ◽

10.1007/s10589-013-9601-4 ◽

2013 ◽

Vol 57 (3) ◽

pp. 703-729 ◽

Author(s):

Tuğba Akman ◽

Hamdullah Yücel ◽

Bülent Karasözen

Keyword(s):

Optimal Control ◽

Error Analysis ◽

Optimal Control Problems ◽

A Priori ◽

Diffusion Equations ◽

Control Problems ◽

Interior Penalty ◽

Convection Diffusion ◽

A Priori Error Analysis

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