solucion: Funci<c3><b3>n Soluci<c3><b3>n

In Paquete2018-3/MetodosNumericos: MetodosNumericos

Description

Esta funci<c3><b3>n resuelve el sistema de ecuaciones diferenciales, es llamada dentro de la funci<c3><b3>n principal ODE_Sys con el fin de hallar los valores que conforman la soluci<c3><b3>n.

Usage

solucion (d, vars, init, h, n, method, point)

Arguments

d	Representa al vector de las ecuaciones diferenciales que componen el sistema a solucionar. Ejemplo -> ["Eqn1","Eqn2","Eqn3", ...]
vars	Representa al vector con los nombre de la variables incluyendo la variable independiente (t) al final del vector. Ejemplo -> ["x1","x2","x3", ...,"t"]
init	Vector con los valores iniciales incluyendo la variable indepediente (t) al final del vector. Ejemplo -> [x1_0,x2_0,x3_0, ...,t_0]
h	Constante.
n	N<c3><ba>mero de puntos de la soluci<c3><b3>n que se requieren.
method	M<c3><a9>todo para encontrar la soluci<c3><b3>n. Se encoge entre las siguientes opciones -> ["euler","midpoint",rk4"]
point	Punto deseado para evaluar la soluci<c3><b3>n.

Details

La soluci<c3><b3>n claramente depender<c3><a1> principalmente del m<c3><a9>todo a implantar para resolver el sistema de ecuaciones diferenciales.

Value

La funci<c3><b3>n retorna una lista de valores correspondientes a la soluci<c3><b3>n num<c3><a9>rica para cada valor de la variable independiente.

Author(s)

Pablo Millan y Oscar Fonseca

Examples

# Ejemplos:
#sol=solucion(c("x*y","x*y-1"),c("x","y","t"),c(0.5,0.5,0),0.1,500,"euler",0.62)
#sol=solucion(c("x*y","x*y-1"),c("x","y","t"),c(-2,1,0),0.01,400,"midpoint",0.5)
#sol=solucion(c("x*y","x*y-1"),c("x","y","t"),c(-2,2,0),0.01,700,"rk4",0.674)
#sol=solucion(c("x-y+z","x*y-1","z+3*x"),c("x","y","z","t"),c(0,1,1,0),0.01,450,"euler",0.5)
##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## The function is currently defined as
Solucion <- function(d, vars, init, h, n, method, point){
  if (method=="euler"){
    values=matrix(init,ncol = 1)

    for (i in 1:length(d)){
      assign(vars[i],init[i])
    }

    npoints=1
    values=cbind(values,numeric(length(d)+1))

    while (npoints<n) {
      for (i in 1:length(d)){
        values[i,npoints+1]=values[i,npoints]+h*eval(parse(text=d[i]))
      }

      for (i in 1:length(d)){
        assign(vars[i],values[i,npoints+1])
      }

      values[length(d)+1,npoints+1]=values[length(d)+1,npoints]+h

      assign(vars[length(d)+1],values[length(d)+1,npoints+1])

      values=cbind(values,numeric(length(d)+1))
      npoints=npoints+1

    }

    values=values[,-npoints-1]
  }

  if (method=="midpoint"){
    values=matrix(init,ncol = 1)

    for (i in 1:length(d)){
      assign(vars[i],init[i]+h/2)
    }

    npoints=1
    values=cbind(values,numeric(length(d)+1))

    while (npoints<n) {
      for (i in 1:length(d)){
        values[i,npoints+1]=values[i,npoints]+h*eval(parse(text=d[i]))
      }

      for (i in 1:length(d)){
        assign(vars[i],values[i,npoints+1]+h/2)
      }

      values[length(d)+1,npoints+1]=values[length(d)+1,npoints]+h

      assign(vars[length(d)+1],values[length(d)+1,npoints+1])

      values=cbind(values,numeric(length(d)+1))
      npoints=npoints+1

    }

    values=values[,-npoints-1]
  }

  if (method=="rk4"){
    values=matrix(init,ncol = 1)

    for (i in 1:length(d)){
      assign(vars[i],init[i]+h/2)
    }

    npoints=1
    values=cbind(values,numeric(length(d)+1))

    while (npoints<n) {
      k1=numeric(length(d))
      k2=numeric(length(d))
      k3=numeric(length(d))
      k4=numeric(length(d))

      for (i in 1:length(d)){
        k1[i]=h*eval(parse(text=d[i]))
        assign(vars[i],values[i,npoints]+k1[i]/2)
      }
      for (i in 1:length(d)){
        k2[i]=h*eval(parse(text=d[i]))
        assign(vars[i],values[i,npoints]+k2[i]/2)
      }
      for (i in 1:length(d)){
        k3[i]=h*eval(parse(text=d[i]))
        assign(vars[i],values[i,npoints]+k3[i])
      }
      for (i in 1:length(d)){
        k4[i]=h*eval(parse(text=d[i]))
      }
      for (i in 1:length(d)){
        values[i,npoints+1]=values[i,npoints]+ k1[i]/6 + k2[i]/3 + k3[i]/3 + k4[i]/6
      }
      for (i in 1:length(d)){
        assign(vars[i],values[i,npoints+1])
      }
      values[length(d)+1,npoints+1]=values[length(d)+1,npoints]+h
      assign(vars[length(d)+1],values[length(d)+1,npoints+1])

      values=cbind(values,numeric(length(d)+1))
      npoints=npoints+1
    }
    values=values[,-npoints-1]
  }
  return (values)
}



{ ~kwd1 }
{ ~kwd2 }

Paquete2018-3/MetodosNumericos documentation built on May 4, 2019, 7:36 a.m.