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05-08-2020-Resolução-equaçao
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# Minimo para resolver equação f(x)=0. f<-function(u){ # Definição de função f(u), para resolver a equação f(u)=0 x=u[1];y=u[2] c(exp(x+y)-2, sin(x)+cos(y)-1) } g<-function(u){ t(f(u)) %*% f(u)/2 } gradng<-function(u){ h=0.00000001 v=u; v[1]=u[1]+h dgx=(g(v)-g(u))/h w=u; w[2]=u[2]+h dgy=(g(w)-g(u))/h c(dgx,dgy) } # Método de Euler ZeroEuler<-function(u0,t,n){ u=u0 h=t/n for (i in 1:n){u=u-h*gradng(u)} u } # Teste u0=c(0,0); t=100; n=1000 u=ZeroEuler(u0,t,n) ; u # Aproximadamente u(100) f(u) g(u)
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