fsolve - Maple Programming Help

fsolve

solve one or more equations using floating-point arithmetic

 Calling Sequence fsolve( equations, variables, complex )

Parameters

 equations - equation, set(equation), expression, set(expression), list(equation), procedure, list(procedure) variables - (optional) name or set(name); unknowns for which to solve complex - (optional) literal name; search for complex solutions

Basic Information

Description

 • The fsolve command numerically computes the zeroes of one or more equations, expressions or procedures.

Output

 • The solutions to a single equation are returned as an expression sequence.
 • The solutions to a set or list of equations are returned as sets of equation sequences.
 • For a single polynomial equation of one variable with real coefficients, by default the fsolve command computes all real (non-complex) roots. It may not return all roots for exceptionally ill-conditioned polynomials.
 • For a single polynomial equation of one variable with some (non-real) complex coefficients, the fsolve command computes all real and complex roots. It may not return all roots for exceptionally ill-conditioned polynomials.
 • For a general equation or system of equations, the fsolve command computes a single real root.

Examples

A Polynomial Equation in One Variable

 For a univariate real polynomial equation, the fsolve command computes all real solutions.
 > $\mathrm{polynomial}≔2{x}^{5}-11{x}^{4}-7{x}^{3}+12{x}^{2}-4x=0:$
 > $\mathrm{fsolve}\left(\mathrm{polynomial}\right)$
 ${-}{1.334383488}{,}{0.}{,}{5.929222024}$ (1)

Other Equations

 For more complicated equations, the fsolve command computes one real solution.
 > $\mathrm{polynomials}≔\left\{3{x}^{4}{y}^{2}=17,{x}^{3}y-5x{y}^{2}-2y=1\right\}:$
 > $\mathrm{fsolve}\left(\mathrm{polynomials}\right)$
 $\left\{{x}{=}{2.118203038}{,}{y}{=}{0.5305528603}\right\}$ (2)
 > $\mathrm{fsolve}\left(\mathrm{tan}\left(\mathrm{sin}\left(x\right)\right)=1\right)$
 ${0.9033391108}$ (3)
 > $f≔\mathrm{sin}\left(x+y\right)-{ⅇ}^{x}y=0:$
 > $g≔{x}^{2}-y=2:$
 > $\mathrm{fsolve}\left(\left\{f,g\right\}\right)$
 $\left\{{x}{=}{-}{6.017327250}{,}{y}{=}{34.20822723}\right\}$ (4)
 If an equation has no real solutions or you are interested in complex solutions then you can search for a complex solution using the complex option. For equations and expressions, the complex option must be preceded by the variables option.
 > $\mathrm{fsolve}\left(\mathrm{ln}\left(v\right)={v}^{2}\right)$
 ${\mathrm{fsolve}}{}\left({\mathrm{ln}}{}\left({v}\right){=}{{v}}^{{2}}{,}{v}\right)$ (5)
 > $\mathrm{fsolve}\left(\mathrm{ln}\left(v\right)={v}^{2},v,\mathrm{complex}\right)$
 ${0.6143632454}{-}{0.6810654878}{}{I}$ (6)
 > $\mathrm{fsolve}\left(\mathrm{ln}\left(v\right)-{v}^{2},v,\mathrm{complex}\right)$
 ${0.6143632454}{-}{0.6810654878}{}{I}$ (7)
 > $\mathrm{fsolve}\left(t→\mathrm{ln}\left(t\right)-{t}^{2},\mathrm{complex}\right)$
 ${0.6143632454}{-}{0.6810654878}{}{I}$ (8)

Details

 For detailed information including:
 • Complete description of all parameters
 • Complete description of functionality
 • Specifying ranges or initial points
 • Shortcuts for specifying equations and unknowns
 • Specifying you want to find complex roots
 • Limiting the number of solutions returned for a polynomial equation of one variable
 see the fsolve/details help page.