Solving ODEs with Heun's Method: A Question

Click For Summary
SUMMARY

This discussion centers on the application of Heun's Method for solving ordinary differential equations (ODEs), specifically the equation du/dt = au. The user outlines the formula y(new) = y(old) + 0.5(k1 + k2)Δh, where k1 is defined as f(y(old)) and k2 as f(y(old) + q11k1Δh) with q11 equal to 1. The confusion arises regarding the multiplication of the k2 term by 'a', which is clarified as a misunderstanding by the user, who ultimately resolves the issue independently.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with numerical methods, specifically Heun's Method
  • Basic calculus, particularly differentiation
  • Knowledge of function notation and evaluation
NEXT STEPS
  • Study the derivation and application of Heun's Method in numerical analysis
  • Explore other numerical methods for solving ODEs, such as Runge-Kutta methods
  • Learn about stability and error analysis in numerical solutions of ODEs
  • Investigate the use of software tools like MATLAB or Python's SciPy for implementing Heun's Method
USEFUL FOR

Students and professionals in mathematics, engineering, and physics who are interested in numerical methods for solving ordinary differential equations, particularly those using Heun's Method.

yugeci
Messages
61
Reaction score
0
Hi there,

in my notes for Heun's method for solving an ODE, I have

y(new) = y(old) + 0.5(k1 + k2)Δh

And k1 is supposed to be f(y(old)) while k2 is f(y(old) + q11k1Δh) and q11 is 1

So if for example I have a simple differential equation like du/dt = au

It would be du/dt = 0.5(k1 + k2)

du/dt = 0.5(au(told) + a((u(told)+au(told)Δt))

The first term on the right of the equal is k1, and the term after is k2. What I don't understand is why the entire k2 term is multiplied by a? It's not in any formula so what mistake have I made here. I couldn't really find this in any of my books either, especially since the notation is so different.
 
Physics news on Phys.org
I figured it out. This thread can be deleted.
 

Similar threads

Graduate Optimization of a nonlinear system
  • · Replies 5 ·
Replies
5
Views
2K
Graduate How can I solve a coupled PDE and ODE using the method of lines?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Solving Non-Linear ODEs with RK4 Method: Time Step Considerations
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Fortran programming to solve ODEs
  • · Replies 1 ·
Replies
1
Views
4K
Quantum Tunelling Problem with Boundary Conditions
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Two-Mass Oscillator: Plotting Amplitudes Over Frequency in Hertz
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Question about solving linear first order non-homogeneous ODEs
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Seeking advice about solving an ODE
  • · Replies 3 ·
Replies
3
Views
3K
Comp Sci Solving 2nd Order DEs with 4th Order RK Method
  • · Replies 4 ·
Replies
4
Views
2K
Graduate How to solve ODE for independent function
  • · Replies 2 ·
Replies
2
Views
3K