Basic Numerical Analysis

This repository consist of MATLAB implementation of Numerical Algorithms that are taught in a first course of Numerical Analysis.
All implementation are written in form of functions and can be called directly.

Index

1. Introduction to MATLAB

• Factorial of positive integer n(factposnum) ☑
• First n fibonacci numbers(fibn) ☑
• First number n for which factorial(n) has i digits(firstidig) ☑

2. Nonlinear Equations in One Variable

• Bisection Method(bisection_method) ☑
• Newton Rapshon's Method(nr_method) ☑
• Secant Method(secant_method) ☑
• Modified Newton's Method(mnr_method) ☑

3. Linear Systems: Direct Method

• Ax=b, A is diagonal matrix(diag_solver) ☑
• Forward Substitution Method(fs_method) ☑
• Backward Substitution Method(bs_method)
• Gauss Elimination Method(ge_method)
• Gauss Elimination with Partial Pivoting(gewpp_method)
• Gauss Jordan Method(gj_method)
• LU Decompositon(Doolittle's Factorisation)(doo_method)
• LU Decompositon(Cholesky Method)(chol_method)

4. Linear Systems: Iterative Method

• Gauss-Jacobi Method(gjacob_method)
• Gauss-Seidel Method(gseidel_method)

5. Interpolation

• Lagrange Polynomial(lagrange_inter) ☑

6. Numerical Integration

• Midpoint Method(mp_method) ☑
• Composite Midpoint Method(cmp_method) ☑
• Trapezoidal Rule(trap_rule) ☑
• Composite Trapezoidal Rule(ctrap_rule) ☑
• Simpson Rule(simpson_rule) ☑
• Composite Simpson Rule(csimpson_rule) ☑
• One point Gauss Quadrature(opgq_method) ☑
• Two point Gauss Quadrature(tpgq_method) ☑

7. Numerical Solution of Differential Equation

• Forward Euler's Method(fe_method) ☑
• Modified Euler's Method(mfe_method) ☑
• Runge Kutta Method of Order 2(rk2) ☑
• Runge Kutta Method of Order 4(rk4) ☑