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1 @c Copyright (C) 1996, 1997 John W. Eaton |
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2 @c This is part of the Octave manual. |
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3 @c For copying conditions, see the file gpl.texi. |
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4 |
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5 @node Nonlinear Equations |
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6 @chapter Nonlinear Equations |
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7 @cindex nonlinear equations |
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8 @cindex equations, nonlinear |
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9 |
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10 Octave can solve sets of nonlinear equations of the form |
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11 @iftex |
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12 @tex |
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13 $$ |
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14 f (x) = 0 |
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15 $$ |
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16 @end tex |
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17 @end iftex |
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18 @ifinfo |
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19 |
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20 @example |
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21 F (x) = 0 |
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22 @end example |
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23 @end ifinfo |
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24 |
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25 @noindent |
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26 using the function @code{fsolve}, which is based on the @sc{Minpack} |
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27 subroutine @code{hybrd}. |
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28 |
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29 @DOCSTRING(fsolve) |
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30 |
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31 @DOCSTRING(fsolve_options) |
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32 |
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33 Here is a complete example. To solve the set of equations |
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34 @iftex |
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35 @tex |
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36 $$ |
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37 \eqalign{-2x^2 + 3xy + 4\sin(y) - 6 &= 0\cr |
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38 3x^2 - 2xy^2 + 3\cos(x) + 4 &= 0} |
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39 $$ |
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40 @end tex |
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41 @end iftex |
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42 @ifinfo |
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43 |
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44 @example |
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45 -2x^2 + 3xy + 4 sin(y) = 6 |
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46 3x^2 - 2xy^2 + 3 cos(x) = -4 |
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47 @end example |
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48 @end ifinfo |
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49 |
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50 @noindent |
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51 you first need to write a function to compute the value of the given |
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52 function. For example: |
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53 |
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54 @example |
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55 function y = f (x) |
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56 y(1) = -2*x(1)^2 + 3*x(1)*x(2) + 4*sin(x(2)) - 6; |
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57 y(2) = 3*x(1)^2 - 2*x(1)*x(2)^2 + 3*cos(x(1)) + 4; |
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58 endfunction |
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59 @end example |
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60 |
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61 Then, call @code{fsolve} with a specified initial condition to find the |
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62 roots of the system of equations. For example, given the function |
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63 @code{f} defined above, |
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64 |
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65 @example |
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66 [x, info] = fsolve ("f", [1; 2]) |
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67 @end example |
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68 |
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69 @noindent |
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70 results in the solution |
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71 |
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72 @example |
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73 x = |
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74 |
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75 0.57983 |
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76 2.54621 |
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77 |
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78 info = 1 |
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79 @end example |
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80 |
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81 A value of @code{info = 1} indicates that the solution has converged. |
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82 |
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83 The function @code{perror} may be used to print English messages |
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84 corresponding to the numeric error codes. For example, |
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85 |
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86 @example |
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87 @group |
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88 perror ("fsolve", 1) |
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89 @print{} solution converged to requested tolerance |
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90 @end group |
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91 @end example |
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92 |
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93 |
