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A semi-linear delayed diffusion-wave system with distributed order in time

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Abstract
A numerical scheme for a class of non-linear distributed order fractional diffusion-wave equations with fixed time delay is considered. The focus lies on the derivation of a linearized compact difference scheme as well as on quantitatively analyzing it. We prove unique solvability, convergence and stability of the resulted numerical solution in $L_{\infty}$-norm by means of the discrete energy method. Numerical examples are introduced to illustrate the accuracy and efficiency of the proposed method.
Keywords
Distributed order fractional diffusion-wave equations, Linear difference scheme, Discrete energy method, Delayed partial differential equations, Convergence, Stability, COMPACT DIFFERENCE SCHEME, POPULATION-MODEL, BOUNDED DOMAINS, EQUATIONS

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Citation

Please use this url to cite or link to this publication:

MLA
Hendy, Ahmed S, Rob De Staelen, and Vladimir G Pimenov. “A Semi-linear Delayed Diffusion-wave System with Distributed Order in Time.” JOURNAL OF NUMERICAL ALGORITHMS 77.3 (2018): 885–903. Print.
APA
Hendy, A. S., De Staelen, R., & Pimenov, V. G. (2018). A semi-linear delayed diffusion-wave system with distributed order in time. JOURNAL OF NUMERICAL ALGORITHMS, 77(3), 885–903.
Chicago author-date
Hendy, Ahmed S, Rob De Staelen, and Vladimir G Pimenov. 2018. “A Semi-linear Delayed Diffusion-wave System with Distributed Order in Time.” Journal of Numerical Algorithms 77 (3): 885–903.
Chicago author-date (all authors)
Hendy, Ahmed S, Rob De Staelen, and Vladimir G Pimenov. 2018. “A Semi-linear Delayed Diffusion-wave System with Distributed Order in Time.” Journal of Numerical Algorithms 77 (3): 885–903.
Vancouver
1.
Hendy AS, De Staelen R, Pimenov VG. A semi-linear delayed diffusion-wave system with distributed order in time. JOURNAL OF NUMERICAL ALGORITHMS. 2018;77(3):885–903.
IEEE
[1]
A. S. Hendy, R. De Staelen, and V. G. Pimenov, “A semi-linear delayed diffusion-wave system with distributed order in time,” JOURNAL OF NUMERICAL ALGORITHMS, vol. 77, no. 3, pp. 885–903, 2018.
@article{8520283,
  abstract     = {A numerical scheme for a class of non-linear distributed order fractional diffusion-wave equations with fixed time delay is considered. The focus lies on the derivation of a linearized compact difference scheme as well as on quantitatively analyzing it. We prove unique solvability, convergence and stability of the resulted numerical solution in $L_{\infty}$-norm by means of the discrete energy method. Numerical examples are introduced to illustrate the accuracy and efficiency of the proposed method.},
  author       = {Hendy, Ahmed S and De Staelen, Rob and Pimenov, Vladimir G},
  issn         = {1017-1398},
  journal      = {JOURNAL OF NUMERICAL ALGORITHMS},
  keywords     = {Distributed order fractional diffusion-wave equations,Linear difference scheme,Discrete energy method,Delayed partial differential equations,Convergence,Stability,COMPACT DIFFERENCE SCHEME,POPULATION-MODEL,BOUNDED DOMAINS,EQUATIONS},
  language     = {eng},
  number       = {3},
  pages        = {885--903},
  title        = {A semi-linear delayed diffusion-wave system with distributed order in time},
  url          = {http://dx.doi.org/10.1007/s11075-017-0344-7},
  volume       = {77},
  year         = {2018},
}

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