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Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

Tikekar, VG and Prabhu, S (1970) Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem. In: Proceedings of the Indian Academy of Sciences - Section A, 71 (6). pp. 288-297.

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Abstract

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Item Type: Journal Article
Additional Information: Copyright of article belongs to Indian Academy of Sciences.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 28 May 2010 10:11
Last Modified: 19 Sep 2010 06:07
URI: http://eprints.iisc.ernet.in/id/eprint/28149

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