README

Numerical Methods

1. Extended False Position

False Position Formula:

$c_i=b_i-\frac { f(b_i)(b_i-a_i)} { f(b_i)-f(a_i) }$

for i = 0,1,2,…..,M

  For finding multiple roots simultaneously of the function at the interval.

This app use extended algorithm than classical False position method.

Build in Lazarus 3.2.

Use lib:

1. Art formula as math parser to input math equation at runtime.
2. Chart as graph viewer.

2. Multi-Critical Point Finder

Using Extended Golden Search Method:

&nbsp&nbsp&nbsp To find multiple critical points (maximum and minimum) of the function simultaneously.

Build in Lazarus 3.2.

Use lib:

1. Art formula as math parser to input math equation at runtime.
2. Chart as graph viewer.

3. Multi-Intersection Point Finder

Using Extended False Position Method:

&nbsp&nbsp&nbsp To find multiple intersection points between two graphs/functions simultaneously.

When two graphs intersected, Y1=Y2 so Y1-Y2=0, it's a finding root problem that can be solved using one of the finding root methods, in this case using False position method.

If we had been got the root(x), then input x into one of the equation (Y1 or Y2), so we got (x,y) as the intersection coordinate.

This app will be found multiple intersection points, so the method need to be extended becomes Extended False Position method.

Build in Lazarus 3.2.

Use lib:

1. Art formula as math parser to input math equation at runtime.
2. Chart as graph viewer.

4. Multi-Area Calculation using Extended False Position Method and Extended Composite Simpson’s 1/3 Rule

False Position Formula:

$c_i=b_i-\frac { f(b_i)(b_i-a_i)} { f(b_i)-f(a_i) }$

for i = 0,1,2,…..,M

Composite Simpson’s 1/3 Rule Formula:

$\int_{a}^{b}f(x)dx\approx\frac{h}{3} \left[ f(x_0)+2\sum_{k=1}^{\frac{M}{2}-1}f(x_{2k})+4\sum_{k=1}^{\frac{M}{2}}f(x_{2k-1})+f(x_M)\right]$

h=(b-a)/M ; x0 =a ; xM= b ; xk=a+k h ; for k=0,1,2…M

  To simultaneously calculate the multi-area under the curve and between two curves of the function on the given interval.

Build in Lazarus 3.2.

Use lib:

1. Art formula as math parser to input math equation at runtime, the component/lib on the folder "formula".
2. Chart as graph viewer.

5. Integral Double & Integral Equation Solver

Using Simpson's 1/3 rule:

&nbsp&nbsp&nbsp To find double integral of function I=f(x,y) and Integral Equation.

$I=\int_{y1}^{y2}\int_{x1}^{x2}f(x,y) dxdy$

Build in Delphi 7

6. File Nix NumericVer3.2.apk

This is an app android for solving math problem using numerical methods.

MENU :

1. GRAPHIC

2. ROOT-FINDING

       2.1. BISECTION

       2.2. FALSE POSITION

       2.3. SECANT

       2.4. NEWTON-RAPHSON etc

3. OPTIMIZATION

4. NUMERICAL INTEGRATION

5. NUMERICAL DIFFERENTIATION

6. LINEAR SYSTEM

7. EIGENPAIRS

8. INTERPOLATION

9. CURVE-FITTING

10. ODEs

11. PDEs

Each menu got submenu.

Download on:

https://github.com/nix97/Numerical-Methods/releases/download/numerical/Nix.NumericVer3.2.apkk

7. File Nix Numeric.rar

This is an app windows for solving math problem using numerical methods.

The menu just like app android above.

Download on:

https://github.com/nix97/Numerical-Methods/releases/download/numerical2/Nix.Numeric.rarr