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We wish to solve equation (5)
by a method involving **splitting**.
Since equation (5)
is an unfamiliar one,
we turn to the **heat-flow equation**
which besides being familiar, has no complex numbers.
A two-sentence derivation of the **heat-flow equation** follows.
(1) The heat
flow *H*_{x} in the *x*-direction equals the
negative of the gradient of
temperature *T* times the heat conductivity .(2) The decrease of temperature is
proportional to the divergence
of the heat flow divided by
the heat storage capacity *C* of the
material.
Combining these, extending from one
dimension to two, taking constant and ,gives the equation
| |
(6) |

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Stanford Exploration Project

12/26/2000