The subject of various math problems, mostly solved using Numerical methods.

1. Partial Differential Equations(PDEs)

The coverage of these problem is:

• Wave equation using Finite-Difference method.
• Heat equation using Forward-Difference method.
• Laplace's equation Dirichlet method.
• Poisson's equation using Finite-Difference method.

2. System of Ordinary Differential Equation using Runge-Kutta fourth-order formula(RK4)

Solving of First-Order Two Differential Equation Y'(t)=F(t,x,y) and X'(t)=F(t,x,y) IVP(Initial Value Problem)

3. Third-Order Differential Equation

using Runge-Kutta fourth-order formula(RK4)

Diff equation Y'''(t)=F(t,y,y',y'') use IVP(Initial Value Problem)

4. Conversion Number

Build in Lazarus 1.6.4 is an app for converting number from base to base (binary, octal, decimal, hexadecimal).

5. Matrix Determinant

Build in Lazarus 1.6.4 is an app for finding Determinant of Matrix using LU Decomposition.

6. Wave Equation

Finite-Difference Solution for the Wave Equation Utt(t,x) = c^2 Uxx(t,x) It's using GUI on matlab. In this problem using algorithm, not use built-in function from toolbox.

7. Linear Shooting Method

To approximate the solution of the boundary value problem (bvp) x '' = p(t) x'(t) + q(t) x(t) + r(t) with x(a) = alpha and x(b) = beta over the interval [a , b], subinterval M by using the Runge-Kutta method of order 4.

8. Matrix Solver

To solve matrix problems such as Multiplication, Determinant, Invers, Linear System, Eigenpairs and Singular Value Decomposition(SVD).

9.Second-order ODE Solver using Runge-Kutta-Fehlberg (RKF45)

To solving initial value problem (ivp) second-order Ordinary Differential Equation(ODE) using Runge-Kutta-Fehlberg formula (RKF45). This formula got advantages than the RK4 classic, RKF45 have Error Estimation. In this python project, use math parser pymep, so we can input equation at runtime.

10. Eigenpairs Fullset

Jacobi Iteration for Eigenvalues and Eigenvectors To compute the full set of Eigenpairs ( Eigenvalues λ and Eigenvector V ) of the Real symmentrical matrix A.

Eigenproblem is A V = λ V

11. Gauss Jordan for solving Systems of Linear Equations

This app for solving Systems of Linear Equations (AX=B) using Gauss Jordan method.

12. AES

It's about cryptography using Advance Encryption Standard(AES). Key size 128, 192, 256 bits This part use library System.Security.Cryptography. App in GUI.

13. ODEs Solver

FIRST-ORDER ODE(IVP)

First-Order Ordinary Differential Equation (ivp) using Runge-Kutta 4th Order(RK4) method.

To approximate the solution of the initial value problem (ivp) y ' =f(x,y) with y(a)=yo over [a,b] and subinterval M.

14. Geometry Transformation

This app for Basic Transformation of Geometry. The transformation are Translation, Rotation and Scaling.

15. Polynomial Division

To dividing Polynomial by other Polynomial On the way : Dividend = Quotient x Divisor + Remainder

16. Area of Irregular Polygon

App for counting Area of Irregular Polygon. For counting this problem using Heron's formula.

Another works(Math stuff ,app and sourcecode on https://bitbucket.org/nixz97/nix/downloads/)

Created by Lukas Setiawan
e-mail: lukassetiawan@yahoo.com
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