Title 
Summary 
Primary Author 
Date 

Function trapz(a, b, n) approximates the integral of f(x) in the interval [a; b] using the trapezoidal composite rule. n is the number of subintervals. 
Alain kapitho 
20060120 

The solution to a system of nonlinear equations may be found with fixed_point_systems(x0, N). As in the case of a single nonlinear equation, the system compactly written as F(x) = 0, has to be rewritten in the subfunction as x = G(x). The output consists 
Alain kapitho 
20060111 

Function fixed_point(p0, N) attempts to find the solution of an equaion f(x) = 0, that the user has to rewrite in the fixedpoint form x = g(x). The iterative scheme is then x(k+1) = g(x(k)) and implemented N times, starting with an initial approximation 
Alain kapitho 
20060111 

The function allows to solve simultaneoulsy different linear systems with the same coefficient matrix A using the GaussJordan algorithm 
Alain kapitho 
20051115 

Function Gauss_Seidel(A, b, N) iteratively solves a system of linear equations whereby A is the coefficient matrix, b the righthand side column vector and N the maximum number of iterations. A transition/iteration matrix approach is implemented, with Tg 
Alain kapitho 
20070814 

Solving a nbyn linear system of equations using Gaussian elimination with partial pivoting 
Alain kapitho 
20051118 

Function Jacobi(A, b, N) iteratively solves a system of linear equations whereby A is the coefficient matrix, b the righthand side column vector and N the maximum number of iterations. As with the Gauss_Seidel(A, b, N) function, a transition matrix appro 
Alain kapitho 
20070814 

Given n points in xy coordinates, function Least_Squares(x, y, m) constructs the leastsquares polynomial of degree m. The call to the function returns a vector c whose components c0, c1, ..., cm are the coefficients of the polynomial. 
Alain kapitho 
20060111 

given n points in xy coordinates, function divided_diff(x,y,x0) constructs the Newton's interpolatory polynomial of degree n1 and evaluates it at the specified point x0. 
Alain kapitho 
20060111 

Function rk4_systems(a, b, N, alpha) approximates the solution of a system of differential equations, by the method of Rungekutta order 4.
a and b are the endpoints of the interval, N the number of subdivisions, and alpha the initial conditions 
Alain kapitho 
20060120 

Given an initialvalue problem of the form y' = f(t,y), function runge_kutta4(a, b, N, alpha) approximates its solution in the interval [a; b] using the RungeKutta method of order 4. 
Alain kapitho 
20060111 

Function simps(a, b, n) approximates the integral of f(x) using the composite Simpson rule. The user needs to specify f(x) as a subfunction at the bottom of the file 
Alain kapitho 
20060120 

Function SOR(A,b,N) solves iteratively the linear system Ax = b, N being the maximum number of iterations. Iterations are implemented in matrix form as x(k+1) = Tw*x(k) + c, with Tw being the transition/iteration matrix and c a constant vector. the optim 
Alain kapitho 
20070814 