Using Newton's Method to Solve Nonlinear Equation in Matlab

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1. A MATLAB function fnewton is supplied for Newton’s method. The function that forms
   
2. the left side of the equation we wish to solve and its derivative must be supplied by the
   
3. user as functions; these become the first and second parameters of the function. The third
   
4. parameter is an initial approximation to the root. The convergence criterion used is that
   
5. the difference between successive approximations to the root is less than a small preset
   
6. value. This value must be supplied by the user and is given as the fourth parameter of the
   
7. function.
   
8. function [res, it] = fnewton(func,dfunc,x,tol)
   
9. % Finds a root of f(x) = 0 using Newton
   
10. s method.
    
11. % Example call: [res, it] = fnewton(func,dfunc,x,tol)
    
12. % The user defined function func is the function f(x).
    
13. % The user defined function dfunc is df/dx.
    
14. % x is an initial starting value, tol is required accuracy.
    
15. it = 0; x0 = x;
    
16. d = feval(func,x0)/feval(dfunc,x0);
    
17. while abs(d) > tol
    
18. x1 = x0-d; it = it+1; x0 = x1;
    
19. d = feval(func,x0)/feval(dfunc,x0);
    
20. end
    
21. res = x0;
    
22. We will now find a root of the equation
    
23. x3 􀀀10x2 C29x􀀀20 D 0
    
24. To use Newton’s method we must define the function and its derivative as follows:
    
25. >> f = @(x) x.^3-10*x.^2+29*x-20;
    
26. >> df = @(x) 3*x.^2-20*x+29;
    
27. We may call the function fnewton as follows:
    
28. >> [x,it] = fnewton(f,df,7,0.00005)
    
29. x =
    
30. 5.0000
    
31. it =
    
32. 6

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Reference

• Numerical Methods using Matlab Abhishek Gupta Apress
  

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关键词：Nonlinear equation nonlinea Nonline Linear difference function equation supplied between