Adding custom euler function and pracma library for half-life

Schrick-Noah_Homework-3.R

@@ -39,10 +39,47 @@ plot(abs(log(central.diff.table[,"h"],10)), central.diff.table[,"error"],
 
 ## 2.
 # a) Runge-Kutta
+my_rk4 <- function(f, y0, t0, tfinal, dt){
+  
+}
 
 # b) Numerically solve the decay ode and compare to Euler and RK error
+decay.f <- function(t,y,k){
+  # define the ode model
+  # k given value when solver called
+  dydt <- -k*y
+  as.matrix(dydt) 
+}
+
+# From class docs:
+my_euler <- function(f, y0, t0, tfinal, dt){
+  # follow ode45 syntax, dt is extra
+  # y0 is initial condition
+  tspan <- seq(t0,tfinal,dt)
+  npts <- length(tspan)
+  y<-rep(y0,npts) # initialize, this will be a matrix for systems
+  for (i in 2:npts){
+    dy <- f(t[i-1],y[i-1])*dt # t is not used in this case
+    y[i] <- y[i-1] + dy
+  }
+  return(list(t=tspan,y=y))
+}
 
 ## 3. Use library function ode45 to solve the decay numerically
+if (!require("pracma")) install.packages("pracma")
+library(pracma)
+# specify intial conds and params
+k <- 1.21e-4
+tmin <- 0
+tmax <- 10000
+y.init <- 10000
+
+decay.ode45.sol <- ode45(f=function(t,y){decay.f(t,y,k=k)},
+                         y=y.init, t0=tmin, tfinal=tmax)
+plot(decay.ode45.sol$t,decay.ode45.sol$y)
+par(new=T)
+lines(seq(tmin,tmax,len=50),
+      y.init*exp(-k*seq(tmin,tmax,len=50)))
 
 ## 4. Solve the predator-prey model numerically