Problem with solve two differential equations.

In summary, the conversation is about solving two equations involving the variables y, v, and t. The first equation relates the change in yv over time to a function f, while the second equation involves the constant change in v over x. The person asking for help is unsure about the properties of y, the function f, and the variables to solve for. They clarify that y is a variable that changes with time, v is mesh velocity, x is displacement, and h is an element length in finite element. They are attempting to solve for y and v at each time step.
  • #1
hoomanya
90
0
Hi,

I am trying to solve the two equations cited below but not sure if it is possible to solve them...

∂(yv)/∂t=f(y,v,t)
where v is velocity = dx/dt, and y is a material property.

In addition:
∂v/∂x = constant

Any hints would be appreciated.

Many Thanks!
 
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  • #2
Well... i would like to help, but there are some things i could not understand.

Is y a constant, or it is a function of v, t, or some other variable?

Is f(y,v,t) a given (known) function? (like f(y,v,t)=sin(y+v*t) for example)

And what are the variables you are trying to solve for?
 
  • #3
Hi,
y is a variable , say density and changes with time.
v is mesh velocity and and x is displacement. When I said ∂v/∂x = constant, I meant ∂v/∂h = constant, where h could be thought of as an element length in finite element. I'm not sure if that would make a difference.
I am trying to solve for y and v at each time step.
Thank you very much.
 

FAQ: Problem with solve two differential equations.

What is the definition of a differential equation?

A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It is used to model dynamic systems and find the values of the function at different points.

What is the difference between an ordinary and partial differential equation?

An ordinary differential equation involves a single independent variable, while a partial differential equation involves multiple independent variables. Ordinary differential equations are used for single-variable systems, while partial differential equations are used for multi-variable systems.

How do you solve a system of two differential equations?

To solve a system of two differential equations, you can use various methods such as separation of variables, substitution, or the method of undetermined coefficients. It is important to identify the type of equations and choose the appropriate method.

What is the significance of solving a system of differential equations?

Solving a system of differential equations allows us to predict the behavior of complex systems over time. It is useful in various fields such as physics, engineering, and economics to model and analyze real-world problems.

How do you verify the solution of a system of differential equations?

To verify the solution of a system of differential equations, you can substitute the solution into the original equations and check if it satisfies them. You can also use numerical methods to approximate the solution and compare it to the exact solution.

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