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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