A system of two second order differential equations

In summary, the conversation discusses the best method for solving two coupled second order differential equations by hand without using built-in functions in Matlab. The initial conditions include displacement and velocity both being 0, with an initial acceleration dependent on pressure over time. The conversation also touches on the possibility of using Euler integration and RK4 codes to compare results. It is also mentioned that the equations can be put into four first order equations for easier solving.
  • #1
jeffro06
4
0
I was wondering what the best method is to solve two second order differential equations that are coupled. I need to solve it by hand and write my own code so I cannot use built in functions in matlab, etc. At time (0), displacement and velocity are 0 with an initial acceleration which is dependent on pressure as a function of time.
 
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  • #2
Perhaps a little more detail would be helpful. Are these ordinary DEs? Linear? Homogeneous?
 
  • #3
...and...

Is it a computational project?

What language do you use?

fwiw, if it is, just write a simple Euler integration code (after putting the equations into first order form), see if it works and then compare with results from an RK4 code...
 
  • #4
I didn't know that I could put them into 4 first order equations, but I did it and it worked fine. Thank you.
 

1. What is a system of two second order differential equations?

A system of two second order differential equations is a set of two equations that involve one or more dependent variables and their derivatives with respect to a single independent variable. These equations are commonly used to model dynamic systems in science and engineering.

2. How is a system of two second order differential equations solved?

There are several methods for solving a system of two second order differential equations, including the elimination method, substitution method, and matrix methods. These methods involve manipulating the equations algebraically to solve for the unknown variables.

3. What is the importance of a system of two second order differential equations?

A system of two second order differential equations is important because it allows us to model and understand complex dynamic systems in various fields, such as physics, engineering, and biology. These equations can provide insight into the behavior of these systems and help us make predictions.

4. Can a system of two second order differential equations have multiple solutions?

Yes, a system of two second order differential equations can have multiple solutions. This can occur when the equations are nonlinear or when the initial conditions are not well-defined. In some cases, there may also be infinite solutions or no solutions at all.

5. How are initial conditions used in solving a system of two second order differential equations?

Initial conditions, also known as boundary conditions, are used to determine a unique solution to a system of two second order differential equations. These conditions specify the values of the dependent variables at a given point in time, which allows us to find a specific solution that satisfies the equations.

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