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Engineering Computation

Engineering Computation. Part 2: Exercises. Bisection Method. function [res]=f(x) res=7500-1000.*(1-(1+x).^(-20))./x;. % This is the MainBisection program xl=0.0000001; xu=1; es=0.00002; imax=50; xx=linspace(xl,xu,20); yy=f(xx); plot(xx,yy); hold on

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Engineering Computation

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  1. EngineeringComputation Part 2: Exercises E. T. S. I. Caminos, Canales y Puertos

  2. Bisection Method function [res]=f(x) res=7500-1000.*(1-(1+x).^(-20))./x; % This is the MainBisection program xl=0.0000001; xu=1; es=0.00002; imax=50; xx=linspace(xl,xu,20); yy=f(xx); plot(xx,yy); hold on [Bisect ea iter]=Bisection(xl,xu,es,imax); fprintf('Solution: %18.12f Relative error: %18.12f Iterations: %5d\n',Bisect,ea,iter); E. T. S. I. Caminos, Canales y Puertos

  3. Bisection Method function [Bisect ea iter]=Bisection(xl,xu,es,imax); iter=0; fl=f(xl); ea=2*es; xr=xl; while ea>es && iter<=imax xrold=xr; xr=(xl+xu)/2; fr=f(xr); iter=iter+1; if xr ~= 0 ea=abs((xr-xrold)/xr)*100; end test=fl*fr; if test<0 xu=xr; else if test>0 xl=xr; fl=fr; else ea=0; end end fprintf(' xl= %18.8f xu= %18.8f\n',xl,xu); end Bisect=xr; E. T. S. I. Caminos, Canales y Puertos

  4. False Position Method function [res]=f(x) res=7500-1000.*(1-(1+x).^(-20))./x; function [xr ea iter]=FalsePosition(xl,xu,es,imax); iter=0; fl=f(xl); fu=f(xu); ea=2*es; xr=xl; il=0; iu=0; while ea>es && iter<=imax; xrold=xr; xr=xu-fu*(xl-xu)/(fl-fu); fr=f(xr); iter=iter+1; if xr ~= 0 ea=abs((xr-xrold)/xr)*100; end test=fl*fr; if test<0 xu=xr; fu=f(xu); iu=0; il=il+1; if il>=2 fl=fl/2; else if test>0 xl=xr; fl=f(xl); il=0; iu=iu+1; if iu>=2 fu=fu/2; else ea=0; end end end end fprintf(' xl= %18.8f xu= %18.8f\n',xl,xu); end xl=0.0000001; xu=1; es=0.00002; imax=100; xx=linspace(xl,xu,20); yy=f(xx); plot(xx,yy); hold on plot([xl,xu],[0,0],'*'); [xr ea iter]=FalsePosition(xl,xu,es,imax); fprintf('Solution: %18.12f Relative error: %18.12f Iterations: %5d\n',xr,ea,iter); E. T. S. I. Caminos, Canales y Puertos

  5. Fixed Point Method function [res]=f(x) res=7500-1000.*(1-(1+x).^(-20))./x; x0=0.000001; es=0.0000000001; imax=30; [xr ea iter]=FixedPoint(x0,es,imax); fprintf('Solution: %18.12f Relative error: %18.12f Iterations: %5d\n',xr,ea,iter); function [xr ea iter]=FixedPoint(x0,es,imax) xr=x0; iter=0; ea=2*es; while ea>es && iter<=imax xrold=xr; xr=g(xrold); iter=iter+1; if xr ~= 0 ea=abs((xr-xrold)/xr)*100; end fprintf(' xr= %18.8f ea= %18.8f\n',xr,ea); end E. T. S. I. Caminos, Canales y Puertos

  6. Modified Secant Method function [res]=f(x) res=7500-1000.*(1-(1+x).^(-20))./x; x0=0.1; es=0.00002; imax=30; [xr ea iter]=ModifiedSecant(x0,es,imax); fprintf('Solution: %18.12f Relative error: %18.12f Iterations: %5d\n',xr,ea,iter); function [xr ea iter]=ModifiedSecant(x0,es,imax); xr=x0 iter=0; ea=2*es; eps=0.01; while ea>es && iter<=imax xrold=xr; xr=xr-f(xr)/(f(xr+eps)-f(xr-eps))*2*eps; iter=iter+1; if xr ~= 0 ea=abs((xr-xrold)/xr)*100; end fprintf(' xr= %18.8f ea= %18.8f\n',xr,ea); end plot([xr],[0],'*'); E. T. S. I. Caminos, Canales y Puertos

  7. Newton-Raphson Method function [res]=f1(x); res=1000*((1-(1+x).^(-20))./x-20.*(1+i).^(-21))./x; function [res]=f(x) res=7500-1000.*(1-(1+x).^(-20))./x; x0=0.2; es=0.00002; imax=30; [xr ea iter]=NewtonRaphson(x0,es,imax); fprintf('Solution: %18.12f Relative error: %18.12f Iterations: %5d\n',xr,ea,iter); function [xr ea iter]=NewtonRaphson(x0,es,imax) xr=x0; iter=0; ea=2*es; while ea>es && iter<=imax xrold=xr; xr=xr-f(xr)/f1(xr); iter=iter+1; if xr ~= 0 ea=abs((xr-xrold)/xr)*100; end fprintf(' xr= %18.8f ea= %18.8f\n',xr,ea); end; E. T. S. I. Caminos, Canales y Puertos

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