# Solving non-linear equations simultaneously with DE's using Euler integration

• Jigby
In summary: John,and whether you eqtion a stiff one?Yeah, MATLAB has some stiff solvers as well. One thing that could happen with ODE45 is it could take too long to integrate if it ends up needing to take too small a step size to get the required error tolerance. One way to get around this is to decrease the error tolerances in ODE45. Eular's method may get you a solution but I don't know how you can be sure it is sufficiently accurate.
Jigby
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:
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.

Why would you want to do that? Are you doing a real time application or something or a homework question. Do you require very fast integration? Anyway, you can always write your own function. Euler's method is pretty basic.

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.

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.

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.

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.

i agree with John,and whether you eqtion a stiff one?

Yeah, MATLAB has some stiff solvers as well. One thing that could happen with ODE45 is it could take too long to integrate if it ends up needing to take too small a step size to get the required error tolerance. One way to get around this is to decrease the error tolerances in ODE45. Eular's method may get you a solution but I don't know how you can be sure it is sufficiently accurate.

## 1. What is the purpose of solving non-linear equations simultaneously with DE's using Euler integration?

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.

## 2. What is a non-linear equation?

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.

## 3. What is a differential equation (DE)?

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.

## 4. How does Euler integration work in solving non-linear equations simultaneously with DE's?

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.

## 5. What are the limitations of solving non-linear equations simultaneously with DE's using Euler integration?

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.

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