A computationally efficient scheme for the non-linear diffusion equation
This Letter proposes a new numerical scheme for integrating the non-linear diffusion equation. It is shown that it is linearly stable. Some tests are presented comparing this scheme to a popular decentered version of the linearized Crank–Nicholson scheme, showing that, although this scheme is slight...
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| Veröffentlicht in: | Physics letters. A 2009-04, Vol.373 (17), p.1573-1577 |
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| container_title | Physics letters. A |
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| creator | Termonia, P. Van de Vyver, H. |
| description | This Letter proposes a new numerical scheme for integrating the non-linear diffusion equation. It is shown that it is linearly stable. Some tests are presented comparing this scheme to a popular decentered version of the linearized Crank–Nicholson scheme, showing that, although this scheme is slightly less accurate in treating the highly resolved waves, (i) the new scheme better treats highly non-linear systems, (ii) better handles the short waves, (iii) for a given test bed turns out to be three to four times more computationally cheap, and (iv) is easier in implementation. |
| doi_str_mv | 10.1016/j.physleta.2009.02.059 |
| format | Article |
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A</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Termonia, P.</au><au>Van de Vyver, H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A computationally efficient scheme for the non-linear diffusion equation</atitle><jtitle>Physics letters. A</jtitle><date>2009-04-01</date><risdate>2009</risdate><volume>373</volume><issue>17</issue><spage>1573</spage><epage>1577</epage><pages>1573-1577</pages><issn>0375-9601</issn><eissn>1873-2429</eissn><abstract>This Letter proposes a new numerical scheme for integrating the non-linear diffusion equation. It is shown that it is linearly stable. Some tests are presented comparing this scheme to a popular decentered version of the linearized Crank–Nicholson scheme, showing that, although this scheme is slightly less accurate in treating the highly resolved waves, (i) the new scheme better treats highly non-linear systems, (ii) better handles the short waves, (iii) for a given test bed turns out to be three to four times more computationally cheap, and (iv) is easier in implementation.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.physleta.2009.02.059</doi><tpages>5</tpages></addata></record> |
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| ispartof | Physics letters. A, 2009-04, Vol.373 (17), p.1573-1577 |
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| language | eng |
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| source | Access via ScienceDirect (Elsevier) |
| subjects | Atmospheric models Diffusion Nonlinear instability Numerics |
| title | A computationally efficient scheme for the non-linear diffusion equation |
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