Method of Lines for Third Order Partial Differential Equations

DOI: 10.4236/jamp.2014.22005   PDF   HTML   XML   2,785 Downloads   5,659 Views   Citations

Abstract

The method of lines is applied to the boundary-value problem for third order partial differential equation. Explicit expression and order of convergence for the approximate solution are obtained.

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Kudu, M. and Amirali, I. (2014) Method of Lines for Third Order Partial Differential Equations. Journal of Applied Mathematics and Physics, 2, 33-36. doi: 10.4236/jamp.2014.22005.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] A. I. Kozhanov, “Mixed Boundary Value Problem for Some Classes of Third Order Differential Equations,” Matematicheskii Sbornik, Vol. 118 (160), No. 4 (8), 1982, pp. 504-522. (in Russian)
[2] A. I. Kozhanov, “Mixed Problem for One Class of Quasilinear Equation of Third Order,” In: Boundary Value Problems for Nonlinear Equations, Novosibirsk, 1982, pp. 118-128. (in Russian)
[3] S. A. Gabov and A. G. Sveshnikov, “Problems of the Dynamics of Stratified Fluids,” Nauka, Moscow, 1986, p. 288. (in Russian)
[4] G. M. Amiraliyev and P. Okcu, “Error Estimates for Differential Difference Schemes to Pseudo-Parabolic Initial-Boundary Value Problem with Delay,” Computers & Mathematics with Applications, Vol. 18, No. 3, 2013, pp. 283-292.
[5] S. B. Nemchinov, “On the Finite Difference Method to the Elliptic Boundary Value Problems,” Journal of Computational and Applied Mathematics, Vol. 2, 1962, pp. 418-436. (in Russian)
[6] A. A. Samarskii, “The Theory of Difference Schemes,” Marcel Dekker, New York, 2001.

  
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