IJPAM: Volume 87, No. 4 (2013)

A STUDY ON UNCONDITIONALLY STABLE EXPLICIT
DIFFERENCE SCHEMES FOR THE VARIABLE
COEFFICIENTS PARABOLIC DIFFERENTIAL EQUATION

Masaharu Nakashima
Kagoshima-Shi
Taniyama Chuou 1-4328, 891-0141, JAPAN


Abstract. In [2], we have presented some new algorithms for solving the linear variable coefficients parabolic differential equations. The proposed scheme is stable without any restriction to step-sizes of space and time. The scheme is required the condition of step size ratio ${k\over h^2},\to 0 $ as $ k,h \to 0$ in the convergence, where $k$ and $h$ are step sizes for space and time respectively. In this paper, we will present the explicit unconditional stable scheme which has no restriction on the step size ratio ${k\over h^2}$ in the convergence. We will also present analysis for the present scheme.

Received: June 15, 2013

AMS Subject Classification: 65L06, 65L07

Key Words and Phrases: Runge-Kutta methods, method of lines, difference equation

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DOI: 10.12732/ijpam.v87i4.8 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 87
Issue: 4