Geodesic
An explicit difference scheme for non-linear heat conduction equation
Matematičeskoe modelirovanie, Tome 34 (2022) no. 12, pp. 3-19

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We develop an algorithm for numerical treatment of non-linear heat conduction problems, which is well adapted to the architecture of high-performance computing systems. The technique is based on hyperbolic heat conduction model and explicit difference scheme. The new scheme provides second order temporal resolution of non-linearity with acceptable time step. An application to plasma dynamic simulations is discussed.
Keywords: non-linear heat conduction equation, hyperbolic heat conduction model, explicit difference scheme, high-performance computing. 
@article{MM_2022_34_12_a0,
     author = {B. N. Chetverushkin and O. G. Olkhovskaya and V. A. Gasilov},
     title = {An explicit difference scheme for non-linear heat conduction equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--19},
     publisher = {mathdoc},
     volume = {34},
     number = {12},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2022_34_12_a0/}
}
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B. N. Chetverushkin; O. G. Olkhovskaya; V. A. Gasilov. An explicit difference scheme for non-linear heat conduction equation. Matematičeskoe modelirovanie, Tome 34 (2022) no. 12, pp. 3-19. http://geodesic.mathdoc.fr/item/MM_2022_34_12_a0/