Mathematic / 5 Mathematical modeling

Birtaeva Z.B.

Kostanay poly technical college, Kostanay

Approximate method for definition

heat conductivity coefficient

We will set initial approach, and the following approach is defined from a condition of minimization of functionality, where temperature and moisture preset values on an earth surface.

We will consider consecutive values of coefficient of heat conductivity and at we will designate the system Decision through, and at we will designate through. We will designate a difference of these sizes through

For simplification of record we will sometimes apply designations.

Then for a difference the differential task also turns out

(1)

(2)

(3)

(4)

For brevity statements are used further designations

, .

Differential task with the return time

We assume that. Then considering initial and boundary conditions (2), we remove .

In the right part of an equal-sign we summarize the second sum in parts on a variable. Collecting similar sizes in the left part of an equal-sign, we will receive:

(5)

Now, we will increase (3) on and we summarize on all internal knots of a grid. We summarize in parts on a variable and.

, then, have next:

Considering a uniform boundary condition and applying a formula, summation in parts, we remove

This work studies temperature and soil moisture on the surface of the land is determined by the thermal conductivity of soils by the method of nets.