1st order ODE with sampled function

  • Context: Graduate 
  • Thread starter Thread starter tamzam
  • Start date Start date
  • Tags Tags
    Function Ode
Click For Summary
SUMMARY

The discussion centers on numerically solving a first-order ordinary differential equation (ODE) defined as v'(x) = b.[v(x) - f(x)], with the boundary condition v(+infinity) = 0, where f(x) is sampled on a dense x grid. The recommended approach is to utilize the standard 4th order Runge-Kutta method for this numerical solution. Participants are encouraged to consult standard texts on numerical solutions or perform a Google search for further details on the Runge-Kutta method.

PREREQUISITES
  • Understanding of first-order ordinary differential equations (ODEs)
  • Familiarity with numerical methods, specifically the Runge-Kutta method
  • Knowledge of boundary value problems in differential equations
  • Experience with sampled functions and interpolation techniques
NEXT STEPS
  • Study the implementation of the 4th order Runge-Kutta method in Python or MATLAB
  • Explore techniques for interpolating sampled functions
  • Research boundary value problem solvers and their applications
  • Learn about error analysis in numerical methods for ODEs
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are working on numerical solutions of differential equations, particularly those dealing with sampled functions and boundary conditions.

tamzam
Messages
1
Reaction score
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...
 
Physics news on Phys.org
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.
 

Similar threads

Undergrad Converting Second Order ODE to Hypergeometric Function
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Existence of unique solutions to a first order ODE on this interval
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Solving Coupled First Order ODEs: Is There a Closed Form Solution?
  • · Replies 28 ·
Replies
28
Views
3K
Graduate Green's function for Sturm-Louiville ODE
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad 2nd order ODE's, variation of parameters and the notorious constraint
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Seeking advice about solving an ODE
  • · Replies 3 ·
Replies
3
Views
3K
Graduate ODE -> Transfer Function Assistance
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Correct Upper/Lower limits for continuation of solutions for ODE
  • · Replies 0 ·
Replies
0
Views
4K
Graduate Searching for radial part solution of Klein-Gordon type equation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Solve second order linear differential equation
  • · Replies 7 ·
Replies
7
Views
2K