Successive Substitution vs Newton's Method

In summary, the disadvantages of the Successive Method compared to Newton's Method for solving nonlinear equations include the potential for divergence, the lack of a clear formulation for guaranteed conversion, and performance dependence on the recursion equation. Additionally, Successive Method may be slower to converge and may not be able to find all solutions to the original equation. However, further research into Newton's Method may provide additional insights and improvements in these areas.
  • #1
DODGEVIPER13
672
0

Homework Statement


Name disadvantages of the Successive Method vs Newtons for solving nonlinear equations?


Homework Equations





The Attempt at a Solution


I went all through the textbook and this is all I could find on the successive method disadvantages but these are not compared to Newtons.

Successive Method-

May diverge

Recursion equation formulation that
guarantees conversion not obvious

Performance depends on recursion
equation

What am I missing or am I correct?
 
Physics news on Phys.org
  • #2
"conversion" ← "convergence"

ss is typically slow to converge, though just occasionally you may fluke a fast-converging rearrangement

if there exist multiple solutions to the original equation, you may never manage to discover those creative rearrangements sometimes necessary to lead to finding every solution

(With ss you can't gauge how close you are to the solution when slowly approaching it from one side, and I suspect that Newton's method may have an improvement on this, but I forget. That may be something you can investigate.)

You'd probably get a slew of responses if you posted this in the maths homework forum .
 
Last edited:
  • Like
Likes 1 person
  • #3
Ok man well I think your stuff is good enough I can research from here.
 

Related to Successive Substitution vs Newton's Method

1. What is the difference between Successive Substitution and Newton's Method?

Successive Substitution is an iterative method used to find an approximation of a root of a function. It involves repeatedly plugging in a value for the variable until the resulting output is close to the actual root. Newton's Method, on the other hand, uses the derivative of the function to find a more precise estimate of the root with each iteration.

2. Which method is more accurate: Successive Substitution or Newton's Method?

Newton's Method is generally considered to be more accurate than Successive Substitution. This is because it uses the slope of the function at each iteration, allowing for a more precise estimate of the root. However, both methods may produce different results depending on the function and the starting value chosen.

3. How do I know which method to use?

The choice between Successive Substitution and Newton's Method depends on the specific problem at hand. Newton's Method is generally faster and more accurate, but it requires knowledge of the derivative of the function. If the derivative is not easily calculable, then Successive Substitution may be a better option.

4. Can Successive Substitution or Newton's Method fail to converge?

Yes, both methods can fail to converge to a root. This can happen if the starting value is too far from the actual root, or if the function has multiple roots. In some cases, a combination of both methods may be used to improve the chances of convergence.

5. Are there any other methods for finding roots of a function?

Yes, there are several other methods for finding roots of a function, such as the Bisection Method, Secant Method, and Fixed Point Iteration. Each method has its own advantages and limitations, and the most appropriate method to use depends on the specific problem at hand.

Similar threads

Using Newton's Method to Solve and Using Fsolve in Matlab
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
How should I Approach this Circuit Calculation?
    • Engineering and Comp Sci Homework Help
Replies
7
Views
925
Truss Method of Joints: Solving Unequal Member Forces
    • Engineering and Comp Sci Homework Help
Replies
2
Views
1K
Newton's Method for Equations of Motion (Vibrations) help?
    • Engineering and Comp Sci Homework Help
Replies
1
Views
3K
Solving Matlab Newton's Method Homework
    • Engineering and Comp Sci Homework Help
Replies
1
Views
2K
How Do You Implement Root-Finding for Compressibility Factors in MATLAB?
    • Engineering and Comp Sci Homework Help
Replies
2
Views
2K
Computing integral using Monte Carlo method
    • Engineering and Comp Sci Homework Help
Replies
12
Views
2K
Finding roots using Newton's method in MATLAB
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Comp Sci C++ programming, Newtons Method.
    • Engineering and Comp Sci Homework Help
Replies
8
Views
5K
MHB Solving Equations Using Bisection, Newton, and Secant Methods
    • General Math
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top