Numerical Methods Calculator in C

A console-based numerical methods calculator developed in the C programming language.

The application provides multiple numerical analysis methods for root finding, matrix operations, solving linear equation systems, numerical differentiation, and numerical integration.

Features

• Polynomial input using coefficients and exponents
• Bisection method
• Regula Falsi method
• Newton-Raphson method
• Matrix inversion
• Gauss-Jordan elimination
• Gauss-Seidel iterative method
• Backward numerical differentiation
• Central numerical differentiation
• Forward numerical differentiation
• Simpson's 1/3 rule
• Simpson's 3/8 rule
• Trapezoidal integration
• Console-based menu system

Technologies Used

• C Programming Language
• Numerical Analysis
• Root-Finding Algorithms
• Matrix Operations
• Iterative Methods
• Numerical Differentiation
• Numerical Integration
• Structures
• Arrays
• Standard C Libraries

Implemented Methods

Root-Finding Methods

• Bisection Method
• Regula Falsi Method
• Newton-Raphson Method

These methods approximate the roots of polynomial functions.

Matrix Operations

• Inverse of an N × N matrix
• Gauss-Jordan elimination
• Gauss-Seidel iterative solution

Numerical Differentiation

The program supports:

• Backward difference
• Central difference
• Forward difference

Numerical Integration

The program supports:

• Simpson's 1/3 Rule
• Simpson's 3/8 Rule
• Trapezoidal Rule

Project Structure

numerical-methods-calculator-c/
├── main.c
├── project-report.pdf
└── README.md

How to Run Using Dev-C++

1. Download the repository.
2. Open main.c in Dev-C++.
3. Click Compile & Run.
4. Select a numerical method from the menu.
5. Enter the requested values.

How to Compile Using GCC

Because the program uses the mathematical functions from math.h, compile it with:

gcc main.c -o numerical-methods -lm

How to Run on Windows

numerical-methods.exe

How to Run on Linux or macOS

./numerical-methods

Menu Options

0. Exit
1. Bisection Method
2. Regula Falsi Method
3. Newton-Raphson Method
4. Inverse of an N × N Matrix
5. Gauss-Jordan Elimination
6. Gauss-Seidel Method
7. Numerical Differentiation
8. Simpson's Method
9. Trapezoidal Method
10. Gregory-Newton Interpolation

Polynomial Input Example

For the polynomial:

f(x) = 2x³ - 4x + 1

Enter:

Number of terms: 3

Term 1:
Coefficient: 2
Exponent: 3

Term 2:
Coefficient: -4
Exponent: 1

Term 3:
Coefficient: 1
Exponent: 0

Example Root-Finding Input

For the Bisection Method:

Starting point: 0
Ending point: 2
Epsilon: 0.001
Maximum iterations: 100

Important Notes

• The maximum polynomial term count is currently limited to 10.
• The maximum matrix size is currently limited to 10 × 10.
• Simpson's 1/3 Rule should use an even number of subdivisions.
• Simpson's 3/8 Rule should use a subdivision count divisible by 3.
• Newton-Raphson requires a suitable initial value.
• Some methods may fail when the selected interval or matrix is invalid.
• The Gregory-Newton Interpolation menu option is present, but its implementation is currently incomplete.

Main Functions

• DegerPolynomial() — Evaluates a polynomial at a given value
• bisectionMethod() — Finds a root using the Bisection Method
• regulaFalsiMethod() — Finds a root using the Regula Falsi Method
• newtonRaphsonMethod() — Finds a root using Newton-Raphson
• matrix_inverse() — Calculates a matrix inverse
• performGaussJordanElimination() — Solves linear equations
• gaussSeidelMethod() — Applies the Gauss-Seidel iterative method
• numericalDerivative() — Calculates numerical derivatives
• simpsonMethod() — Applies Simpson's integration rules
• trapezoidalMethod() — Applies the Trapezoidal Rule

Author

Ali Hasanli
Computer Engineering Student