Numerical methods and computer programming, Secant methods Md Nafiz Hossain Department of Civil Engineering.

1. NEUMERICAL METHODS AND COMPUTER PROGRAMMING
CSE - 201
Group: E
172-Day(DD1)
Batch: 5

2. Welcome To Our Presentation
Submitted to :
Department of Civil Engineering
Daffodil International University
Presented By :
S. M. Sayem 163-47-283
Md. Nazrul Islam Molla 172-47-385
Anika Tabassum Momo 172-47-389
Bipasha Akter 172-47-386
Md. Nafiz Hossain 172-47-425
Sabinoor Esha 172-47-430
Mumita Ara Mostafa Shupti 172-47-431
Md. Toriqul Islam 172-47-404

3. Topic : Secant Method
Contents :
Introduction
Methodology
Derivation of Secant Method
Algorithm
Applications
Advantages
Disadvantages

4. Introductions :
In this method roots are found using an algorithm, that
uses succession of roots of secant lines to better
approximate a root of a function. This method can be
thought of as a finite difference of Newton’s Method.

5. Methodology :
A secant line is defined by using two points on graph of a function f(x). It is
necessary to choose these two initial points as xi and xi-1. Then next point xi+1 is
obtained by computing x-value at which the secant line passing through the points
(xi , f(xi )) and (xi-1, f(xi-1)) has a y-coordinate of zero.

6. The secant method can also be derived from
geometry:
The Geometric Similar Triangles
can be written as
On rearranging, the secant method is given as
Derivation of Secant Method :

7. Algorithm :
Calculate the next estimate of the root from two initial guesses
Calculate the next estimate of the root from two initial guesses
Step 1

8. Find if the absolute relative approximate error is greater than
the prespecified relative error tolerance.
If so, go back to step 1, else stop the algorithm.
Also check if the number of iterations has exceeded the
maximum number of iterations.
Step 2

9. Applications :
• Secant method is one of the analytical procedure available to earthquake
engineers for predicting earthquake performance and structures.
• Secant method is used to develop linear dynamic analysis model to have
the potential to influence the behavior of the structure in non-linear
range.
• It is used for non-linear push over analysis, which defines the force-
displacement relationship of the walls in the building under lateral load.

10. • It converges faster than a linear rate so it is more rapidly
convergent.
• Requires two guesses that do not need to bracket the root.
• It doesn’t require use of derivative of a given function because in
some practical cases, derivatives become very hard to find.
• It requires only one function evaluation per iteration as compared to
Newton’s method which requires two.
Advantages :

11. • It may not converge.
• There is no guaranteed error bound for the computed
iterates.
• It is likely to have difficulty if f 0(α) = 0. This
means the x-axis is tangent to the graph of y = f (x)
at x = α.
• Newton’s method generalizes more easily to new
methods for solving simultaneous systems of nonlinear
equations.
Disadvantages :

12. AnyQuestion ?

13. Thank You