State Youngstown University College of Engineering & Technology Civil & Environmental/Chemical Engineering Program
ENGR6924: Computer Based tools for Engineers This session deals with sparse matrices, sparse matrices operations, Complex numbers and Solution to non-linear equations. CH5, CH6 of the textbook
Matrix Operations with SCILAB Solving Non-linear Equations with SCILAB Applications of Non-linear Equations with SCILAB
Polynomials and solutions to polynomial equations Function roots Example //roots of a polynomial c=[23 0 -122 34 -20 0 4 525 -2 11 3] p10 = poly(c,'y','coeff') roots(p10) Solving systems of non-linear equations Function fsolve
fsolve - find a zero of a system of n nonlinear functions Calling Sequence [x [,v [,info]]]=fsolve(x0,fct [,fjac] [,tol]) Parameters x0 : real vector (initial value of function argument). fct : external (i.e function or list or string). fjac : external (i.e function or list or string). tol : real scalar. precision tolerance: termination occurs when the algorithm estimates that the relative error between x and the solution is at most tol. ( tol=1.d-10 is the default value). x : real vector (final value of function argument, estimated zero). v : real vector (value of function at x). info : termination indicator 0 : improper input parameters. 1 : algorithm estimates that the relative between error x and the solution is at most tol. 2 : number of calls to fcn reached
3 : tol is too small. No further improvement in the approximate solution x is possible. 4 : iteration is not making good progress. Description find a zero of a system of n nonlinear functions in n variables by a modification of the powell hybrid method. Jacobian may be provided. 0 = fct(x) w.r.t x.
Example //solving single non-linear equation deff('[y]=f(x)','y=x^3-2*x^2+1') deff('[y]=fp(x)','y=3*x^2-4*x') fsolve(2.0,f) fsolve(2.0,f,fp) fsolve(2.0,f,fp,0.001) fsolve(1.0,f,fp) [x,f_x]=fsolve(-10,f,fp) [x,f_x,msg]=fsolve(-2.0,f)
Solution of two non-linear euations
function [f] = f2(x) //f2(x) = 0, with x = [x(1);x(2)] //represents a system of 2 non-linear equations f(1) = x(1)^2 + x(2)^2 - 50; f(2) = x(1)*x(2) -25...