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 JAMP  Vol.3 No.11 , November 2015
Unconditionally Explicit Stable Difference Schemes for Solving Some Linear and Non-Linear Parabolic Differential Equation
Abstract: We present the numerical method for solution of some linear and non-linear parabolic equation. Using idea [1], we will present the explicit unconditional stable scheme which has no restriction on the step size ratio k/h2 where k and h are step sizes for space and time respectively. We will also present numerical results to justify the present scheme.
Cite this paper: Nakashima, M. (2015) Unconditionally Explicit Stable Difference Schemes for Solving Some Linear and Non-Linear Parabolic Differential Equation. Journal of Applied Mathematics and Physics, 3, 1506-1521. doi: 10.4236/jamp.2015.311176.
References

[1]   Nakashima, M. (2013) A Study on Unconditionally Stable Explicit Difference Schemes for the Variable Coefficients Parabolic Differential Equation. IJPAM, 87, 587-602.
http://dx.doi.org/10.12732/ijpam.v87i4.8

[2]   Du Fort, E.G. and Frankel, E.G. (1953) Stability Conditions in the Numerical Treatment on Parabolic Differential Equations. Mathematical Tables and Other Aids to Computation, 17, 135-152.
http://dx.doi.org/10.2307/2002754

[3]   Schiesser, W.S. (1991) The Numerical Methods of Lines. Academic Press, San Diego.

[4]   Nakashima, M. (2001) Unconditionally Stable Explicit Difference Schemes for the Variable Coefficients Parabolic Differential Equation (II). Processing Techniques and Applications International Conference, Las Vegas, June 2001, 561-569.

[5]   Nakashima, M. (2002) Unconditionally Stable Explicit Difference Schemes for the Variable Coefficients Parabolic Differential Equation (IV). In: Dinov et al., Eds., Numerical Methods and Applications, Lecture Notes in Computer Science, Springer, Vol. 2542, 536-544.

[6]   Nakashima, M. (2003) Unconditionally Stable Explicit Difference Schemes for the Variable Coefficients Two Dimensional Parabolic Differential Equation (V). Journal of Applied Mechanics, 54, 327-341.

 
 
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