Proceedings of the Indian Academy of Sciences - Section A

, Volume 71, Issue 6, pp 288–297

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

  • V. G. Tikekar
  • Swarnalata Prabhu
Article

DOI: 10.1007/BF03049576

Cite this article as:
Tikekar, V.G. & Prabhu, S. Proc. Indian Acad. Sci. (1970) 71: 288. doi:10.1007/BF03049576

Abstract

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the typey″ = 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.

Copyright information

© Indian Academy of Sciences 1970

Authors and Affiliations

  • V. G. Tikekar
    • 1
  • Swarnalata Prabhu
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of ScienceBangalore-12India