Numerical methods are algoritms used to solve compensal problems numerically rather than analytically. MATLAB provides a versatile environment for implementing these methods accesently. This article presents practial examples of how to implement common numerical techniques in MATLAB.

Solving Nonlinear Equations

Te bisection metodid is a simple technique for finding roots of nonlinear equations. MATLAB code for the bisection metode enterves iteratively ulrowing down an interval where the function changes sign.

Exampla MATLAB code:

CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; Function: CLAS1; CLAS1; CLAS3; CLAS3; FLAS3; (x) = x ^ 3 - x - 2

Code: Code: Code: Code; Code: Code; Code: Code; Code: Code; Code: Code 1; Code 1; Code: Code 1; Code 1; CY: CY-CY

Citlivost; tiskopis; matlab a = 1; b = 2; tol = 1e-5; while (b - a) / 2 tiskopis; gt; tol c = (a + b) / 2; if f (c) = 0 break; equif f (a) * f (c) tiskopis; lt; 0 b = c; else a = c; end end root = c; tiskopis;

Numerical Integration

Te trapezoidal rule approximates the integral of a function by divizing the area into trapezoids. MATLAB can implement this method with simple loops or built- in functions.

Exampla MATLAB code:

CLANE1; CLANE1; FLT: 0 CLANE3; CLANE3; Function: CLANE1; CLANE1; CLANE1; CLANE1; CLANE3; FLANE3; f (x) = sin (x)

Code: Code: Code: Code; Code: Code; Code: Code; Code: Code; Code: Code 1; Code 1; Code: Code 1; Code 1; CY: CY-CY

Citlivost; tiskopis; matlab a = 0; b = pi; n = 100; h = (b - a) / n; integral = 0; for i = 1: n x1 = a + (i - 1) * h; x2 = a + i * h; integral = integral + (f (x1) + f (x2))) / 2 * h; end tiskopis; tiskopis;

Solving Differential Rovnice

Euler 's method is a earforward technique for solving inicial value problems for ordinary diferentail equations. MATLAB' s implementation implives updating te solution iteratively.

Exampla MATLAB code:

CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS1; CLAS1; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; CLAS3; Cx = y, with y (0) = 1

Code: Code: Code: Code; Code: Code; Code: Code; Code: Code; Code: Code 1; Code 1; Code: Code 1; Code 1; CY: CY-CY

Citlivost; tiskopis; matlab x0 = 0; y0 = 1; h = 0,1; x _ end = 1; x = x0: h: x _ end; y = nuly (size (x)); y (1) = y0; for i = 1: length (x) -1 y (i + 1) = y (i) + h * y (i); end end end communications; tiskopis;