1st order ODE with sampled function

In summary, the conversation is about numerically solving a first order ODE with a boundary condition and a known constant. The issue is that the function f(x) is not explicitly known, but is sampled at a dense x grid. The person is seeking help and any hints for finding a solution, and it is suggested to use the standard 4th order Runge-Kutta method.
  • #1
tamzam
1
0
Hello,

My question seems to be simple. I would like to numerically solve the following first order ODE to obtain v(x):

v'(x) = b.[v(x) - f(x)] , given boundary condition v(+infinity) = 0 [b is a known constant]

The problem is that f(x) is not known explicitly (f(x) is sampled at a dense x grid).


Can you please help me? any hints will be appreciated...
 
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  • #2
Welcome to Physics Forums :smile:

What is your application? Is this a homework or self-study problem?

The standard 4th order Runge-Kutta method should work here. For details see practically any text on numerical solutions, or try google.
 

What is a 1st order ODE with sampled function?

A 1st order ODE (Ordinary Differential Equation) with sampled function is a type of differential equation that involves a function and its derivatives. The function is defined at discrete points, or samples, and the equation describes the relationship between the function and its derivative at each sample point.

What is the difference between a 1st order ODE with sampled function and a regular ODE?

The main difference is that a 1st order ODE with sampled function deals with a discrete set of points, while a regular ODE deals with continuous functions. This means that the solution to a 1st order ODE with sampled function is a set of values at each sample point, rather than a continuous function.

What is the importance of 1st order ODE with sampled function in science?

1st order ODEs with sampled function are commonly used in scientific and engineering applications to model systems that involve discrete measurements. They are especially useful in situations where only a limited number of measurements are available and a continuous function cannot be accurately determined.

What are some common techniques for solving 1st order ODEs with sampled function?

There are several techniques that can be used to solve 1st order ODEs with sampled function, including numerical methods like Euler's method and Runge-Kutta methods. These methods involve approximating the function and its derivative at each sample point and using them to calculate the function values at the next sample point.

Can 1st order ODEs with sampled function be solved analytically?

In most cases, 1st order ODEs with sampled function cannot be solved analytically. This is because the solution would involve a piecewise function that is difficult to work with. However, in some special cases, an analytical solution may be possible using techniques such as Laplace transforms or Fourier series.

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