A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type

@article{Crank1996APM,
  title={A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type},
  author={J. Crank and P. Nicolson},
  journal={Adv. Comput. Math.},
  year={1996},
  volume={6},
  pages={207-226}
}
A, k, q are known constants. Equation (1) is of the type which arises in problems of heat flow when there is an internal generation of heat within the medium; if the heat is due to a chemical reaction proceeding at each point at a rate depending upon the local temperature, the rate of heat generation is often defined by an equation such as (2). The presence of the non-linear term q(Ow/at) in (1) and the empirical nature, in many cases, of the surface heat transfer function Hi (0), render the… CONTINUE READING
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