Heat equation, initial and boundary numerical conditions

In summary, the conversation involves a request for a heat equation with numerical initial and boundary conditions, and a discussion about creating a correct example. The person asking for help has a basic understanding of the heat equation and has provided a link for reference. They are also experiencing a warning in Mathematica due to conflicting initial and boundary values.
  • #1
LMZ
12
0
Hello to all!

Homework Statement


for testing my program i need a heat equation with numerical initial and boundary conditions:
Derivative[2, 0][f][x, t] == Derivative[0, 1][f][x, t]

f[x, 0] == numerical
f[0, t] == numerical, f[numerical, t] == numerical


PS. to moders: please, if you delete my message, PM me what I've done wrong, thanks!
 
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  • #2
It's not clear what you are asking. You know what the heat equation is, I presume. Why can't you just make up arbitrary initial and boundary values yourself?
 
  • #3
yeap! i think i know what is heat equation: http://en.wikipedia.org/wiki/Heat_equation#Solving_the_heat_equation_using_Fourier_series

for example if i put these:
Code:
init = f[x, 0] == 1
bc = {f[0, t] == 0, f[1, t] == 0}

in mathematica i got this warning:
A warning is generated in this example because the initial conditions and boundary conditions give two different values for the value of f[0,0].

that's why i need correct example!
 

1. What is the heat equation and what does it represent?

The heat equation is a mathematical equation that describes how heat energy is transferred and distributed in a given system. It represents the relationship between the temperature of a system, its thermal conductivity, and the rate of change of heat within the system.

2. What are initial conditions in the context of the heat equation?

Initial conditions refer to the starting values of temperature within the system at a specific point in time. These values are used to solve the heat equation and determine the temperature distribution over time.

3. What are boundary conditions in the context of the heat equation?

Boundary conditions refer to the values of temperature at the boundaries of the system. These conditions are used to determine how heat is transferred in and out of the system and to solve the heat equation.

4. How are numerical methods used to solve the heat equation?

Numerical methods, such as finite difference methods, are used to discretize the heat equation into a set of algebraic equations that can be solved using computers. These methods provide approximate solutions to the heat equation by dividing the system into smaller segments and calculating the temperature at each point.

5. What are some common applications of the heat equation?

The heat equation has a wide range of applications in various fields, including physics, engineering, and finance. Some common applications include heat transfer in buildings and materials, diffusion of chemical compounds, and option pricing in financial markets.

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