Unconditionally Explicit Stable Difference Schemes for Solving Some Linear and Non-Linear Parabolic Differential Equation

Masaharu Nakashima

Kagoshima-shi, Taniyama Chuou 1-4328 891-0141, Japan.

DOI: 10.4236/jamp.2015.311176                

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.

Keywords

Runge-Kutta Methods, Method of Lines, Difference Equation, Non-Linear PDE

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[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.
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