10.13. Equation Solving

CubicFormula
CubicFormula (p)

Compute roots of a cubic (degree 3) polynomial using the cubic formula. The polynomial should be given as a vector of coefficients. That is 4*x^3 + 2*x + 1 corresponds to the vector [1,2,0,4]. Returns a column vector of the three solutions. The first solution is always the real one as a cubic always has one real solution.

See Planetmath, Mathworld, or Wikipedia for more information.

EulerMethod
EulerMethod (f,x0,y0,x1,n)

Use classical Euler's method to numerically solve y'=f(x,y) for initial x0, y0 going to x1 with n increments, returns y at x1.

See Mathworld for more information.

FindRootBisection
FindRootBisection (f,a,b,TOL,N)

Find root of a function using the bisection method.

FindRootFalsePosition
FindRootFalsePosition (f,a,b,TOL,N)

Find root of a function using the method of false position.

FindRootMullersMethod
FindRootMullersMethod (f,x1,x2,x3,TOL,N)

Find root of a function using the Muller's method.

FindRootSecant
FindRootSecant (f,a,b,TOL,N)

Find root of a function using the secant method.

PolynomialRoots
PolynomialRoots (p)

Compute roots of a polynomial (degrees 1 through 4) using one of the formulas for such polynomials. The polynomial should be given as a vector of coefficients. That is 4*x^3 + 2*x + 1 corresponds to the vector [1,2,0,4]. Returns a column vector of the solutions.

The function calls QuadraticFormula, CubicFormula, and QuarticFormula.

QuadraticFormula
QuadraticFormula (p)

Compute roots of a quadratic (degree 2) polynomial using the quadratic formula. The polynomial should be given as a vector of coefficients. That is 3*x^2 + 2*x + 1 corresponds to the vector [1,2,3]. Returns a column vector of the two solutions.

See Planetmath or Mathworld for more information.

QuarticFormula
QuarticFormula (p)

Compute roots of a quartic (degree 4) polynomial using the quartic formula. The polynomial should be given as a vector of coefficients. That is 5*x^4 + 2*x + 1 corresponds to the vector [1,2,0,0,5]. Returns a column vector of the four solutions.

See Planetmath, Mathworld, or Wikipedia for more information.

RungeKutta
RungeKutta (f,x0,y0,x1,n)

Use classical non-adaptive Runge-Kutta method to numerically solve y'=f(x,y) for initial x0, y0 going to x1 with n increments, returns y at x1.

See Mathworld for more information.