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A Special Case on the Stability and Accuracy for the 1D Heat Equation Using 3-Level and θ-Schemes

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DOI: 10.4236/am.2015.63045    3,682 Downloads   4,112 Views   Citations

ABSTRACT

We establish the conditions for the compute of the stability restriction and local accuracy on the time step and we prove the consistency and local truncation error by using θ-scheme and 3-level scheme for Heat Equation with smooth initial conditions and for some parameter θ∈[0,1].

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Alzate, P. , Cardona, J. and Rojas, L. (2015) A Special Case on the Stability and Accuracy for the 1D Heat Equation Using 3-Level and θ-Schemes. Applied Mathematics, 6, 476-483. doi: 10.4236/am.2015.63045.

References

[1] Strikwerda, J.C. (1989) Finite Difference Schemes and Partial Differential Equations. Wadsworth & Brooks, Siam, Madison, Wisconsin.
[2] McRea, G.J. and Godin, W.R. (1967) Numerical Solution of Atmospheric Diffusion for Chemically Reacting Flows. Journal of Computational Physics, 77, 1-42.
[3] Cárdenas Alzate, P.P. (2014) A Survey of the Implementation of Numerical Schemes for Linear Advection Equation. Advances in Pure Mathematics, 4, 467-479.
http://dx.doi.org/10.4236/apm.2014.48052
[4] Cárdenas Alzate, P.P. (2014) A Survey of the Implementation of Numerical Schemes for the Heat Equation Using forward Euler in Time. Journal of Applied Mathematics and Physics, 2, 1153-1158.
http://dx.doi.org/10.4236/jamp.2014.213135
[5] Hundsdorfer, W. and Koren, B. (1995) A Positive Finite-Difference Advection Scheme Applied on Locally Refined Grids. Journal of Computational Physics, 117, 35-36.
http://dx.doi.org/10.1006/jcph.1995.1042
[6] Canuto, C. and Hussaini, M. (1988) Spectral Methods in Fluids Dynamics. Springer Series in Computational Physics, Springer-Verlag, Berlin.
http://dx.doi.org/10.1007/978-3-642-84108-8
[7] Dehghan, M. (2007) The One-Dimensional Heat Equation Subject to a Boundary Integral Specification. Chaos, Solitons & Fractals, 32, 661-675.
http://dx.doi.org/10.1155/MPE.2005.61
[8] Lu, X., et al. (2005) A New Analytical Method to Solve the Heat Equation for a Multi-Dimensional Composite Slab. Journal of Physics, 38, 2873.

  
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