Jigby said:I have 15 equations with 15 unknowns describing a dynamic process. I would like to know how I can conbine solving non-linear equations together with ordinary differential equations (1st and 2nd order) simultaneously, without using ode45, but Euler's method.
Jigby said:Thanks John, I will try that!
My program is based the dynamic response of a system in the time domain. It was for an assignment last year, but I never quite got it to work so I thought I would try again. My prof told us ODE 45 would not work, he didn't say why though.
John Creighto said:Did he say the Eular's method would work? If so I'm surprised. You know that you can give ODE45 a set of points to calculate the state values at.
The purpose of solving non-linear equations simultaneously with DE's using Euler integration is to find solutions to a system of equations that involves both differential equations (DE's) and non-linear equations. This method allows us to numerically approximate the solutions, which can be useful in various fields of science and engineering.
A non-linear equation is an equation where the terms are not proportional to the variables. In other words, the variables in a non-linear equation are raised to powers other than 1 and are multiplied together. Examples of non-linear equations include quadratic equations, exponential equations, and trigonometric equations.
A differential equation (DE) is an equation that involves derivatives of a function. It describes the relationship between a function and its derivatives. DE's are commonly used to model physical systems and phenomena in various fields such as physics, biology, and economics.
Euler integration is a numerical method that approximates the solutions to a system of equations by breaking it down into smaller steps. In solving non-linear equations simultaneously with DE's, Euler integration is used to approximate the values of the variables at each step, which are then used to calculate the next step. This process is repeated until the desired accuracy is achieved.
Euler integration is a simple method and may not always provide accurate results. It can also be computationally expensive for complex systems. Additionally, it can only solve first-order DE's, so more advanced methods are needed for higher-order DE's. Careful consideration and analysis of the system of equations are also necessary to ensure the validity of the results obtained through Euler integration.